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Phase-retrievable operator-valued frames and representations of quantum channels. (English) Zbl 1434.46047

Summary: We examine some connections among phase-retrievable (not necessarily self-adjoint) operator-valued frames, projective group representation frames and representations of quantum channels. We first present some characterizations of phase-retrievable frames for general operator systems acting on both finite and infinite dimensional Hilbert spaces, which generalize the known results for vector-valued frames, fusion frames and frames of Hermitian matrices. For an irreducible projective unitary representation of a finite group, the image system is automatically phase-retrievable and, moreover, it is a point-wisely tight operator-valued frames. We generalize this notion to more general operator-valued frames, and prove that point-wise tight operator-valued frames are exactly the ones that are right equivalent to operator-valued tight frames. For an operator system that represents a quantum channel, we show that phase-retrievability of the system is independent of the choices of the representations of the quantum channel.

MSC:

46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
42C15 General harmonic expansions, frames
81P45 Quantum information, communication, networks (quantum-theoretic aspects)

Software:

PhaseLift
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Full Text: DOI

References:

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