On the von Neumann entropy of certain quantum walks subject to decoherence. (English) Zbl 1204.81107

Summary: We consider a discrete-time quantum walk on the \(N\)-cycle governed by the condition that at every time step of the walk, the option persists, with probability \(p\), of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems corresponding to the space of the coin and the space of the walker must eventually diminish to zero. Put plainly, any level of decoherence greater than zero forces the system to become completely ‘disentangled’ eventually.


81S22 Open systems, reduced dynamics, master equations, decoherence
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
94A17 Measures of information, entropy
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P15 Quantum measurement theory, state operations, state preparations
Full Text: DOI arXiv


[1] DOI: 10.1103/PhysRevB.80.125309
[2] DOI: 10.1103/PhysRevA.78.052316
[3] DOI: 10.1103/PhysRevA.65.032310
[4] DOI: 10.1142/S0219749903000383 · Zbl 1069.81505
[5] DOI: 10.1103/PhysRevA.74.030301
[6] DOI: 10.1088/1751-8113/43/7/075301 · Zbl 1187.82046
[7] Aharanov, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing pp 50– (2001)
[8] DOI: 10.1103/PhysRevA.81.062129
[9] DOI: 10.1103/PhysRevA.73.042302
[10] DOI: 10.1103/PhysRevA.67.042305
[11] DOI: 10.1103/PhysRevA.72.062317
[12] DOI: 10.1016/j.physa.2004.08.070
[13] DOI: 10.1103/PhysRevA.76.042306
[14] DOI: 10.1103/PhysRevE.81.031113
[15] DOI: 10.1103/PhysRevA.74.022310
[16] Konno, Springer-Verlag Lecture Notes in Mathematics 1954 pp 309– (2008) · Zbl 1329.82011
[17] DOI: 10.1103/PhysRevA.67.042315
[18] Kendon, Quantum Communication, Measurement & Computing (QCMC–02) (2002)
[19] Kendon, Mathematical Structures in Computer Science 17 pp 1169– (2006)
[20] DOI: 10.1080/00107151031000110776
[21] DOI: 10.1103/PhysRevA.58.915
[22] DOI: 10.1103/PhysRevA.72.012327
[23] DOI: 10.1103/PhysRevA.66.052319
[24] DOI: 10.1103/PhysRevA.67.042316
[25] DOI: 10.1023/A:1019609420309 · Zbl 1329.82006
[26] DOI: 10.1007/s00220-009-0930-1 · Zbl 1207.81029
[27] DOI: 10.1088/1367-2630/7/1/156
[28] Zurek, Decoherence Poincaré Seminar 2005, Progress in Mathematical Physics pp 1– (2003)
[29] DOI: 10.1088/1367-2630/9/4/087
[30] DOI: 10.1103/PhysRevA.81.032321
[31] Venegas-Andraca, Quantum Walks for Computer Scientists (2008)
[32] DOI: 10.1088/1367-2630/8/5/081
[33] DOI: 10.1103/PhysRevA.77.062302
[34] DOI: 10.1103/PhysRevA.67.032304
[35] DOI: 10.1103/PhysRevLett.91.130602
[36] Ambainis, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing pp 37– (2001)
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