Recent zbMATH articles in MSC 81Phttps://zbmath.org/atom/cc/81P2021-06-15T18:09:00+00:00WerkzeugIs entanglement a probe of confinement?https://zbmath.org/1460.810072021-06-15T18:09:00+00:00"Jokela, Niko"https://zbmath.org/authors/?q=ai:jokela.niko"Subils, Javier G."https://zbmath.org/authors/?q=ai:subils.javier-gSummary: We study various entanglement measures in a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons field theories by means of their dual supergravity descriptions. A generic field theory in this family possesses a mass gap but does not have a linear quark-antiquark potential. For the two limiting values of the parameter, the theories flow either to a fixed point or to a confining vacuum in the infrared. We show that entanglement measures are unable to discriminate confining theories from non-confining ones with a mass gap. This lends support on the idea that the phase transition of entanglement entropy at large-\(N\) can be caused just by the presence of a sizable scale in a theory. and just by itself should not be taken as a signal of confinement. We also examine flows passing close to a fixed point at intermediate energy scales and find that the holographic entanglement entropy, the mutual information, and the \(F\)-functions for strips and disks quantitatively match the conformal values for a range of energies.
Reviewer: Reviewer (Berlin)Secret history. The story of cryptology. 2nd edition.https://zbmath.org/1460.940012021-06-15T18:09:00+00:00"Bauer, Craig P."https://zbmath.org/authors/?q=ai:bauer.craig-pPublisher's description: The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading.
The second edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here.
The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken.
The text is in two parts. Part I presents classic cryptology from ancient times through World War II. Part II examines modern computer cryptology. With numerous real-world examples and extensive references, the author skillfully balances the history with mathematical details, providing readers with a sound foundation in this dynamic field.
Features:
\begin {itemize}
\item Presents a chronological development of key concepts
\item Includes the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson's wheel cipher, Playfair cipher, ADFGX, matrix encryption, Enigma, Purple, and other classic methods
\item Looks at the work of Claude Shannon, the origin of the National Security Agency, elliptic curve cryptography, the data encryption standard, the advanced encryption standard, public-key cryptography, and many other topics
\item New chapters detail SIGABA and SIGSALY, successful systems used during World War II for text and speech, respectively
\item Includes quantum cryptography and the impact of quantum computers
\end {itemize}
See the review of the first edition in [Zbl 1275.94003].
Reviewer: Reviewer (Berlin)On tensor products of CSS codes.https://zbmath.org/1460.810132021-06-15T18:09:00+00:00"Audoux, Benjamin"https://zbmath.org/authors/?q=ai:audoux.benjamin"Couvreur, Alain"https://zbmath.org/authors/?q=ai:couvreur.alainSummary: CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product \(\otimes\) which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given a CSS code \(\mathcal{C}\), we give a criterion which provides a lower bound on the minimum distance of \(\mathcal{C} \otimes \mathcal{D}\) for every CSS code \(\mathcal{D}\). From this criterion arises a generic bound for the minimum distance which is twice larger than the single bound previously known in the literature. We apply these results to study the behaviour of iterated tensor powers of codes. Such sequences of codes are logarithmically LDPC and we prove in particular that their minimum distances tend generically to infinity. More precisely, their minimum distance increases as \(O(n^\alpha)\) for some \(\alpha > 0\), where \(n\) is the code length, while the row weight of their parity -- check matrices grows as \(O(\log(n))\). This entails a rather surprizing fact: even if a CSS code does not have quantum degeneracy, for a large enough \(\ell\), its \(\ell\)-th iterated tensor power does. Different known results are also reinterpretated in terms of tensor products and three new families of LDPC CSS codes are studied.
Reviewer: Reviewer (Berlin)Quantum contextuality of YO-13 rays.https://zbmath.org/1460.810032021-06-15T18:09:00+00:00"Zhou, Jie"https://zbmath.org/authors/?q=ai:zhou.jie.4"Meng, Hui-Xian"https://zbmath.org/authors/?q=ai:meng.huixian"Shang, Wei-Min"https://zbmath.org/authors/?q=ai:shang.wei-min"Chen, Jing-Ling"https://zbmath.org/authors/?q=ai:chen.jinglingSummary: Quantum contextuality, a more general quantum correlation, is an important resource for quantum computing and quantum information processing. Meanwhile, quantum contextuality plays an important role in fundamental quantum physics. Yu and Oh (YO) proposed a proof of the Kochen-Specker theorem for a qutrit with only 13 rays. Here, we further study quantum contextuality of YO-13 rays using the inequality approach. The maximum quantum violation value of the optimal noncontextuality inequality constructed by YO-13 rays is increased to 11.9776 in the four-dimensional system, which is larger than 11.6667 in the qutrit system. The result shows that the set of YO-13 rays has stronger quantum contextuality in the four-dimensional system. Moreover, we provide an all-versus-nothing proof (i.e. Hardy-like proof) to study YO-13 rays without using any inequality, which is easily applied to experimental tests. Our results will further deepen the understanding of YO-13 rays.
Reviewer: Reviewer (Berlin)Holographic renormalization group flow effect on quantum correlations.https://zbmath.org/1460.830782021-06-15T18:09:00+00:00"Park, Chanyong"https://zbmath.org/authors/?q=ai:park.chanyong"Lee, Jung Hun"https://zbmath.org/authors/?q=ai:lee.junghunSummary: We holographically study the finite-size scaling effects on macroscopic and microscopic quantum correlations deformed by excitation and condensation. The excitation (condensation) increases (decreases) the entanglement entropy of the system. We also investigate the two-point correlation function of local operators by calculating the geodesic length connecting two local operators. As opposed to the entanglement entropy case, the excitation (condensation) decreases (increases) the two-point function. This is because the screening effect becomes strong in the background with the large entanglement entropy. We further show that the holographic renormalization leads to the qualitatively same two-point function as the one obtained from the geodesic length.
Reviewer: Reviewer (Berlin)The classification of symmetry protected topological phases of one-dimensional fermion systems.https://zbmath.org/1460.811242021-06-15T18:09:00+00:00"Bourne, Chris"https://zbmath.org/authors/?q=ai:bourne.chris"Ogata, Yoshiko"https://zbmath.org/authors/?q=ai:ogata.yoshikoSummary: We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group \(G\). This index takes values in \(\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})\) with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.
Reviewer: Reviewer (Berlin)Quantum extremal islands made easy. III: Complexity on the brane.https://zbmath.org/1460.810722021-06-15T18:09:00+00:00"Hernandez, Juan"https://zbmath.org/authors/?q=ai:hernandez.juan-p"Myers, Robert C."https://zbmath.org/authors/?q=ai:myers.robert-c"Ruan, Shan-Ming"https://zbmath.org/authors/?q=ai:ruan.shan-mingSummary: We examine holographic complexity in the doubly holographic model introduced in [\textit{H. Z. Chen} et al., J. High Energy Phys. 2020, No. 10, Paper No. 166, 68 p. (2020; Zbl 1456.81332) and ibid. 2020, No. 12, Paper No. 25, 81 p. (2020; Zbl 1457.81084)] to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the brane. Motivated by these results, we propose a generalization of the CV proposal for higher curvature theories of gravity. Further, we provide two consistency checks of our proposal by studying Gauss-Bonnet gravity and \(f(\mathcal{R})\) gravity in the bulk.
Reviewer: Reviewer (Berlin)State convertibility in the von Neumann algebra framework.https://zbmath.org/1460.460482021-06-15T18:09:00+00:00"Crann, Jason"https://zbmath.org/authors/?q=ai:crann.jason"Kribs, David W."https://zbmath.org/authors/?q=ai:kribs.david-w"Levene, Rupert H."https://zbmath.org/authors/?q=ai:levene.rupert-h"Todorov, Ivan G."https://zbmath.org/authors/?q=ai:todorov.ivan-gSummary: We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting of Nielsen's theorem on the convertibility of quantum states under local operations and classical communication (LOCC) schemes. Along the way, we introduce an appropriate generalisation of LOCC operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von Neumann algebras. As an application of our result in the setting of \(\text{II}_1\)-factors, we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of \textit{G. Vidal} [``Entanglement monotones'', J. Modern Opt. 47, 2--3, 355--376 (2000; \url{doi:10.1080/09500340008244048})], thus yielding a new way to quantify entanglement in that context. Building on previous work in the infinite-dimensional setting, we show that trace vectors play the role of maximally entangled states for general \(\text{II}_1\)-factors. Examples are drawn from infinite spin chains, quasi-free representations of the CAR, and discretised versions of the CCR.
Reviewer: Reviewer (Berlin)Entanglement between two disjoint universes.https://zbmath.org/1460.810062021-06-15T18:09:00+00:00"Balasubramanian, Vijay"https://zbmath.org/authors/?q=ai:balasubramanian.vijay"Kar, Arjun"https://zbmath.org/authors/?q=ai:kar.arjun"Ugajin, Tomonori"https://zbmath.org/authors/?q=ai:ugajin.tomonoriSummary: We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an ``island'' on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.
Reviewer: Reviewer (Berlin)Area law of connected correlation function in higher dimensional conformal field theory.https://zbmath.org/1460.810862021-06-15T18:09:00+00:00"Long, Jiang"https://zbmath.org/authors/?q=ai:long.jiangSummary: We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs). The area law shows similar behaviour as black hole entropy or geometric entanglement entropy. It includes a leading term which is proportional to the area of the entanglement surface, and a logarithmic subleading term with degree \(q\). We extract the UV cutoff independent coefficients and discuss various properties of the coefficients.
Reviewer: Reviewer (Berlin)Beyond spacetime. The foundations of quantum gravity.https://zbmath.org/1460.810012021-06-15T18:09:00+00:00"Huggett, Nick (ed.)"https://zbmath.org/authors/?q=ai:huggett.nick"Matsubara, Keizo (ed.)"https://zbmath.org/authors/?q=ai:matsubara.keizo"Wüthrich, Christian (ed.)"https://zbmath.org/authors/?q=ai:wuthrich.christian.1Publisher's description: One of the greatest challenges in fundamental physics is to reconcile quantum mechanics and general relativity in a theory of quantum gravity. A successful theory would have profound consequences for our understanding of space, time, and matter. This collection of essays written by eminent physicists and philosophers discusses these consequences and examines the most important conceptual questions among philosophers and physicists in their search for a quantum theory of gravity. Comprising three parts, the book explores the emergence of classical spacetime, the nature of time, and important questions of the interpretation, metaphysics, and epistemology of quantum gravity. These essays will appeal to both physicists and philosophers of science working on problems in foundational physics, specifically that of quantum gravity.
The articles of this volume will be reviewed individually.
Reviewer: Reviewer (Berlin)Entanglement entropy: non-Gaussian states and strong coupling.https://zbmath.org/1460.810492021-06-15T18:09:00+00:00"Fernández-Melgarejo, José J."https://zbmath.org/authors/?q=ai:fernandez-melgarejo.jose-j"Molina-Vilaplana, Javier"https://zbmath.org/authors/?q=ai:molina-vilaplana.javierSummary: In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability \textit{bonanza} shown by these variational \textit{ansatze} allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the \(\varphi^4\) scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.
Reviewer: Reviewer (Berlin)Entanglement entropy for \(\text{T}\overline{\text{T}}, \text{J}\overline{\text{T}}, \text{T}\overline{\text{J}}\) deformed holographic CFT.https://zbmath.org/1460.830752021-06-15T18:09:00+00:00"Chakraborty, Soumangsu"https://zbmath.org/authors/?q=ai:chakraborty.soumangsu"Hashimoto, Akikazu"https://zbmath.org/authors/?q=ai:hashimoto.akikazuSummary: We derive the geodesic equation for determining the Ryu-Takayanagi surface in \( \mathrm{AdS}_3\) deformed by single trace \(\mu T\overline{T} + {\varepsilon}_+J\overline{T} + {\varepsilon}_-T\overline{J}\) deformation for generic values of \(( \mu, \epsilon_+, \epsilon_-)\) for which the background is free of singularities. For generic values of \(\epsilon_\pm \), Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta \(c\)-function. We comment on various features of these observables in the \(( \mu, \epsilon_+, \epsilon_-)\) parameter space. We discuss the matching at leading order in small \(( \mu, \epsilon_+, \epsilon_-)\) expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.
Reviewer: Reviewer (Berlin)Entanglement spectrum of geometric states.https://zbmath.org/1460.810802021-06-15T18:09:00+00:00"Guo, Wu-zhong"https://zbmath.org/authors/?q=ai:guo.wu-zhongSummary: The reduced density matrix of a given subsystem, denoted by \(\rho_A\), contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state \(\rho_{A,m}\) associated with an eigenvalue \(\lambda\) for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with \(\lambda_0\) which can be seen as an approximate state of \(\rho_A\). The parameter \(\lambda_0\) is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter \(\lambda_0\) is associated with the entanglement entropy of \(A\) and Rényi entropy in the limit \( n \rightarrow \infty \). As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.
Reviewer: Reviewer (Berlin)Extracting Hawking radiation near the horizon of AdS black holes.https://zbmath.org/1460.830522021-06-15T18:09:00+00:00"Saraswat, Krishan"https://zbmath.org/authors/?q=ai:saraswat.krishan"Afshordi, Niayesh"https://zbmath.org/authors/?q=ai:afshordi.niayeshSummary: We study how the evaporation rate of spherically symmetric black holes is affected through the extraction of radiation close to the horizon. We adopt a model of extraction that involves a perfectly absorptive screen placed close to the horizon and show that the evaporation rate can be changed depending on how close to the horizon the screen is placed. We apply our results to show that the scrambling time defined by the Hayden-Preskill decoding criterion, which is derived in Penington's work [\textit{G. Penington}, J. High Energy Phys. 2020, No. 9, Paper No. 2, 84 p. (2020; Zbl 1454.81039)] through entanglement wedge reconstruction is modified. The modifications appear as logarithmic corrections to Penington's time scale which depend on where the absorptive screen is placed. By fixing the proper distance between the horizon and screen we show that for small AdS black holes the leading order term in the scrambling time is consistent with Penington's scrambling time. However, for large AdS black holes the leading order Log contains the Bekenstein-Hawking entropy of a cell of characteristic length equal to the AdS radius rather than the entropy of the full horizon. Furthermore, using the correspondence between the radial null energy condition (NEC) and the holographic c-theorem, we argue that the screen cannot be arbitrarily close to the horizon. This leads to a holographic argument that black hole mining using a screen cannot significantly alter the lifetime of a black hole.
Reviewer: Reviewer (Berlin)Optimizing quantum models of classical channels: the reverse Holevo problem.https://zbmath.org/1460.810102021-06-15T18:09:00+00:00"Loomis, Samuel P."https://zbmath.org/authors/?q=ai:loomis.samuel-p"Mahoney, John R."https://zbmath.org/authors/?q=ai:mahoney.john-r"Aghamohammadi, Cina"https://zbmath.org/authors/?q=ai:aghamohammadi.cina"Crutchfield, James P."https://zbmath.org/authors/?q=ai:crutchfield.james-pSummary: Given a classical channel -- a stochastic map from inputs to outputs -- the input can often be transformed into an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate variable is a quantum state. We determine when and how well quantum simulations of classical channels may improve upon the minimal rates of classical simulation. This inverts Holevo's original question of quantifying the capacity of quantum channels with classical resources: We determine the lowest-capacity quantum channel required to simulate a classical channel. We also show that this problem is equivalent to another, involving the local generation of a distribution from common entanglement.
Reviewer: Reviewer (Berlin)Islands in de Sitter space.https://zbmath.org/1460.830632021-06-15T18:09:00+00:00"Balasubramanian, Vijay"https://zbmath.org/authors/?q=ai:balasubramanian.vijay"Kar, Arjun"https://zbmath.org/authors/?q=ai:kar.arjun"Ugajin, Tomonori"https://zbmath.org/authors/?q=ai:ugajin.tomonoriSummary: We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal ``islands'' in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.
Reviewer: Reviewer (Berlin)Dynamics of local quantum uncertainty among cavity-reservoir qubits.https://zbmath.org/1460.810042021-06-15T18:09:00+00:00"Ali, Mazhar"https://zbmath.org/authors/?q=ai:ali.mazharSummary: We study dynamics of local quantum uncertainty (LQU) for a system of two cavities and two reservoirs. In the start, the cavities are treated as two qubits which are quantum correlated with each other, whereas reservoirs (also qubits) are neither correlated with each other nor with cavities. We answer two main questions in this work. First, how local quantum uncertainty decays from two quantum correlated cavities and grows among reservoirs. The second question is the examination of LQU developed among four qubits and also shed some light on its dynamics. We observe that LQU develops among reservoirs as kind of mirror image to its decay from cavities. For four qubits, we propose how to compute LQU such that the method is intuitive and analytically computable. We find that among four qubits, LQU starts growing from zero to some maximum value and then decays again to zero as the asymptotic state of cavities is completely transferred to reservoirs. We suggest the experimental setup to implement our results.
Reviewer: Reviewer (Berlin)Multi-hop teleportation of \(N\)-qubit state via Bell states.https://zbmath.org/1460.810112021-06-15T18:09:00+00:00"Fatahi, Negin"https://zbmath.org/authors/?q=ai:fatahi.neginSummary: Multi-hop teleportation is a quantum teleportation scheme for transferring quantum states on a large scale. In this paper, a new multi-hop teleportation protocol is investigated for transferring arbitrary \(N\)-qubit states between \(M\)-neighbor nodes. In this scheme, intermediate nodes are connected with each other by symmetric entangled Bell states as quantum channels. First, one-hop teleportation of single-qubit, two-qubit and \(N\)-qubit states are introduced, then this method is generalized to two-hop and multi-hop teleportation for \(N\)-qubit. Also, we calculate the efficiency of this scheme.
Reviewer: Reviewer (Berlin)An improved E-payment protocol based on quantum blind signature without entanglement.https://zbmath.org/1460.810142021-06-15T18:09:00+00:00"Gou, Xiang-Lin"https://zbmath.org/authors/?q=ai:gou.xiang-lin"Shi, Run-Hua"https://zbmath.org/authors/?q=ai:shi.runhua"Shi, Ze"https://zbmath.org/authors/?q=ai:shi.ze"Li, Kun-Chang"https://zbmath.org/authors/?q=ai:li.kun-changSummary: E-payment plays an important role in modern daily life, so the security problem of E-payment has been widely concerned by researchers. In a recent paper [Int. J. Theor. Phys. 57, No. 9, 2657--2664 (2018; Zbl 1451.81202)], the first author et al. presented a trusted third-party E-payment protocol based on quantum blind signature without entanglement. In this paper, we show that there is a serious security flaw in their E-payment protocol. That is, the partial keys will be disclosed by performing a simple attack strategy. Furthermore, we propose an improved E-payment protocol and analyze its security.
Reviewer: Reviewer (Berlin)Island in the presence of higher derivative terms.https://zbmath.org/1460.830622021-06-15T18:09:00+00:00"Alishahiha, Mohsen"https://zbmath.org/authors/?q=ai:alishahiha.mohsen"Astaneh, Amin Faraji"https://zbmath.org/authors/?q=ai:astaneh.amin-faraji"Naseh, Ali"https://zbmath.org/authors/?q=ai:naseh.aliSummary: Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.
Reviewer: Reviewer (Berlin)Entanglement and confinement in coupled quantum systems.https://zbmath.org/1460.810052021-06-15T18:09:00+00:00"Alet, Fabien"https://zbmath.org/authors/?q=ai:alet.fabien"Hanada, Masanori"https://zbmath.org/authors/?q=ai:hanada.masanori"Jevicki, Antal"https://zbmath.org/authors/?q=ai:jevicki.antal"Peng, Cheng"https://zbmath.org/authors/?q=ai:peng.chengSummary: We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-\(q\) limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.
Reviewer: Reviewer (Berlin)A new multi-party quantum private comparison based on \(n\)-dimensional \(n\)-particle GHZ state.https://zbmath.org/1460.810152021-06-15T18:09:00+00:00"Liu, Wen"https://zbmath.org/authors/?q=ai:liu.wen.3|liu.wen|liu.wen.2|liu.wen.1|liu.wen.4"Yin, Han-Wen"https://zbmath.org/authors/?q=ai:yin.han-wenSummary: With the help of a semi-honest third party Calvin, \(n\) parties \(P_1, P_2,\ldots, P_n\) can determine whether all of their private inputs \(X_1, X_2,\ldots, X_n\) are equal or not without leaking any information. In this paper, we present a novel protocol using special quantum unitary operations and \(n\)-dimensional \(n\)-particle GHZ states. The proposed protocol is correct. It can also resist various outside attacks and overcome the problem of information leakage.
Reviewer: Reviewer (Berlin)Four-agent bidirectional quantum controlled teleportation via quantum entanglement swapping.https://zbmath.org/1460.810122021-06-15T18:09:00+00:00"Zhang, Wanbin"https://zbmath.org/authors/?q=ai:zhang.wanbin"Li, Baosheng"https://zbmath.org/authors/?q=ai:li.baoshengSummary: A total of seven qubits are in a maximally entangled state. Using such an entangled state as quantum channel is based on the construction requirements of quantum long-distance communication [\textit{J. Yin} et al., ``Quantum teleportation and entanglement distribution over 100-kilometre free-space channels'', Nature 488, 185--188 (2012; \url{doi:10.1038/nature11332})]. Multi-party quantum channel (QC) should be studied. We put forward three deterministic bidirectional quantum controlled teleportation (BQCT) schemes. To be specific, BQCT can be realized between any two parties in a deterministic manner with another as the control. Alternatively, the BQCT capacity of such state in the given qubit distribution is thus essentially revealed by virtue of the schemes.
Reviewer: Reviewer (Berlin)Bra-ket wormholes in gravitationally prepared states.https://zbmath.org/1460.830592021-06-15T18:09:00+00:00"Chen, Yiming"https://zbmath.org/authors/?q=ai:chen.yiming"Gorbenko, Victor"https://zbmath.org/authors/?q=ai:gorbenko.victor"Maldacena, Juan"https://zbmath.org/authors/?q=ai:maldacena.juan-m.1Summary: We consider two dimensional CFT states that are produced by a gravitational path integral. As a first case, we consider a state produced by Euclidean \( \mathrm{AdS}_2\) evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology. As a second case, we consider a state produced by Lorentzian \( \mathrm{dS}_2\) evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.
Reviewer: Reviewer (Berlin)Anonymous post-quantum cryptocash.https://zbmath.org/1460.810162021-06-15T18:09:00+00:00"Zhang, Huang"https://zbmath.org/authors/?q=ai:zhang.huang"Zhang, Fangguo"https://zbmath.org/authors/?q=ai:zhang.fangguo"Tian, Haibo"https://zbmath.org/authors/?q=ai:tian.haibo"Au, Man Ho"https://zbmath.org/authors/?q=ai:au.man-hoSummary: In this paper, we construct an anonymous and decentralized cryptocash system which is potentially secure against quantum computers. In order to achieve that, a linkable ring signature based on ideal lattices is proposed. The size of a signature in our scheme is \(O(\log N)\), where \(N\) is the cardinality of the ring. The framework of our cryptocash system follows that of CryptoNote with some modifications. By adopting the short quantum-resistant linkable ring signature scheme, our system is anonymous and efficient. We also introduce how to generate the verifying and signing key pairs of the linkable ring signature temporarily. With these techniques, the privacy of users is protected, even though their transactions are recorded in the public ledger.
For the entire collection see [Zbl 1422.94004].
Reviewer: Reviewer (Berlin)Quantum statistical learning via quantum Wasserstein natural gradient.https://zbmath.org/1460.810082021-06-15T18:09:00+00:00"Becker, Simon"https://zbmath.org/authors/?q=ai:becker.simon"Li, Wuchen"https://zbmath.org/authors/?q=ai:li.wuchenSummary: In this article, we introduce a new approach towards the statistical learning problem \(\operatorname{argmin}_{\rho (\theta ) \in{\mathcal{P}}_{\theta }} W_Q^2 (\rho_{\star },\rho (\theta ))\) to approximate a target quantum state \(\rho_{\star }\) by a set of parametrized quantum states \(\rho (\theta )\) in a quantum \(L^2\)-Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional \(C^*\) algebras. For continuous parametric models of density operators, we pull back the quantum Wasserstein metric such that the parameter space becomes a Riemannian manifold with quantum Wasserstein information matrix. Using a quantum analogue of the Benamou-Brenier formula, we derive a natural gradient flow on the parameter space. We also discuss certain continuous-variable quantum states by studying the transport of the associated Wigner probability distributions.
Reviewer: Reviewer (Berlin)Entanglement entropy inequalities in BCFT by holography.https://zbmath.org/1460.830772021-06-15T18:09:00+00:00"Chou, Chia-Jui"https://zbmath.org/authors/?q=ai:chou.chia-jui"Lin, Bo-Han"https://zbmath.org/authors/?q=ai:lin.bohan"Wang, Bin"https://zbmath.org/authors/?q=ai:wang.bin.1|wang.bin.4|wang.bin.3|wang.bin.2|wang.bin"Yang, Yi"https://zbmath.org/authors/?q=ai:yang.yiSummary: We study entanglement entropy inequalities in boundary conformal field theory (BCFT) by holographic correspondence. By carefully classifying all the configurations for different phases, we prove the strong subadditiviy and the monogamy of mutual information for holographic entanglement entropy in BCFT at both zero and finite temperatures.
Reviewer: Reviewer (Berlin)Synchronous linear constraint system games.https://zbmath.org/1460.910582021-06-15T18:09:00+00:00"Goldberg, Adina"https://zbmath.org/authors/?q=ai:goldberg.adinaSummary: Mathematical models of quantum mechanics can be studied and distinguished using nonlocal games. We discuss a class of nonlocal games called synchronous linear constraint system (syncLCS) games. We unify two algebraic approaches to studying syncLCS games and relate these games to nonlocal games played on graphs, known as graph isomorphism games. In more detail, syncLCS games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated with these games encode information about the existence of perfect strategies. They are called the game algebra and the solution group. Here, we show that these objects are essentially the same, i.e., the game algebra is a suitable quotient of the group algebra of the solution group. We also demonstrate that syncLCS games are equivalent to graph isomorphism games on a pair of graphs parameterized by the linear system.
{\copyright 2021 American Institute of Physics}
Reviewer: Reviewer (Berlin)Asymptotic performance of port-based teleportation.https://zbmath.org/1460.810092021-06-15T18:09:00+00:00"Christandl, Matthias"https://zbmath.org/authors/?q=ai:christandl.matthias"Leditzky, Felix"https://zbmath.org/authors/?q=ai:leditzky.felix"Majenz, Christian"https://zbmath.org/authors/?q=ai:majenz.christian"Smith, Graeme"https://zbmath.org/authors/?q=ai:smith.graeme.1"Speelman, Florian"https://zbmath.org/authors/?q=ai:speelman.florian"Walter, Michael"https://zbmath.org/authors/?q=ai:walter.michaelQuantum teleportation is a primitive widely used in quantum information science for transmission of unknown quantum state between systems using shared entanglement, joint measurement, classical communication and correction operation. Port-based teleportation (PBT) is a specific variant of such protocol, when a correction operation of receiver is a choice of one among several subsystems (`ports'). However, PBT may not implement ideal state transfer if number of ports is finite. Fundamental limits of PBT fidelity for arbitrary finite input dimension and a large number of ports are estimated in this work. Authors use methods from representation theory of symmetric and unitary groups for analyse of probability distributions on a set of random matrices necessary to describe the quantum measurement in PBT.
Reviewer: Alexander Yurevich Vlasov (Sankt-Peterburg)Injective continuous frames and quantum detections.https://zbmath.org/1460.420462021-06-15T18:09:00+00:00"Han, Deguang"https://zbmath.org/authors/?q=ai:han.deguang"Hu, Qianfeng"https://zbmath.org/authors/?q=ai:hu.qianfeng"Liu, Rui"https://zbmath.org/authors/?q=ai:liu.ruiIn [\textit{S. Botelho-Andrade} et al., J. Fourier Anal. Appl. 25, No. 5, 2268--2323 (2019; Zbl 1423.42052)], the authors give a complete solution for the quantum injective frame problem and the frame quantum state estimation problem. In the paper under review, the authors consider the continuous frame version of the quantum detection problem.
Reviewer: Paşc Găvruţă (Timişoara)Von Neumann entropy in QFT.https://zbmath.org/1460.810482021-06-15T18:09:00+00:00"Longo, Roberto"https://zbmath.org/authors/?q=ai:longo.roberto"Xu, Feng"https://zbmath.org/authors/?q=ai:xu.fengSummary: In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones \(O \subset \widetilde{O}\) of the spacetime, where the closure of \(O\) is contained in \(\widetilde{O}\). Given a QFT net \(\mathcal{A}\) of local von Neumann algebras \(\mathcal{A}(O)\), we consider the von Neumann entropy \(S_{\mathcal{A}} (O, \widetilde{O})\) of the restriction of the vacuum state to the canonical intermediate type \(I\) factor for the inclusion of von Neumann algebras \(\mathcal{A}(O) \subset \mathcal{A} (\widetilde{O})\) (split property). We show that this canonical entanglement entropy \(S_{\mathcal{A}} (O, \widetilde{O})\) is finite for the chiral conformal net on the circle generated by finitely many free Fermions (here double cones are intervals). To this end, we first study the notion of von Neumann entropy of a closed real linear subspace of a complex Hilbert space, that we then estimate for the local free fermion subspaces. We further consider the lower entanglement entropy \(\underline{S}_{\mathcal{A}} (O, \widetilde{O})\), the infimum of the vacuum von Neumann entropy of \(\mathcal{F}\), where \(\mathcal{F}\) here runs over all the intermediate, discrete type \(I\) von Neumann algebras. We prove that \(\underline{S}_{\mathcal{A}} (O, \widetilde{O})\) is finite for the local chiral conformal net generated by finitely many commuting \(U(1)\)-currents.
Reviewer: Reviewer (Berlin)Erratum to: Chaos and entanglement spreading in a non-commutative gauge theory.https://zbmath.org/1460.830442021-06-15T18:09:00+00:00"Fischler, Willy"https://zbmath.org/authors/?q=ai:fischler.willy"Jahnke, Viktor"https://zbmath.org/authors/?q=ai:jahnke.viktor"Pedraza, Juan F."https://zbmath.org/authors/?q=ai:pedraza.juan-fSummary: We point out minor mistakes appearing in the published version of our paper [the authors, J. High Energy Phys. 2018, No. 11, Paper No. 72, 43 p. (2018; Zbl 1404.83045)]. The main conclusions remain unaffected.
Reviewer: Reviewer (Berlin)