Frame phase retrievability and state distinguishability of quantum channels

• URL: http://arxiv.org/abs/2608.30006v1
• Date: Sun, 30 Aug 2026 20:01:26 GMT
• Title: Frame phase retrievability and state distinguishability of quantum channels
• Abstract summary: This survey introduces the role of frame phase retrieval in pure-state identification and information preservation by quantum channels.<n>For unit vectors, the lift $xmapsto xx*$ identifies vectors that differ only by a global phase with the same rank-one quantum state.<n>From this viewpoint, a channel is phase retrievable exactly when it is injective on pure states.
• Score: 4.092357804635167
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This survey introduces the role of frame phase retrieval in pure-state identification and information preservation by quantum channels. For unit vectors, the lift $x\mapsto xx^*$ identifies vectors that differ only by a global phase with the same rank-one quantum state, converts frame intensities into linear functionals of the lifted state, and makes the adjoint pullback of output observables an operator-valued measurement on the input system. From this viewpoint, a channel is phase retrievable exactly when it is injective on pure states. We develop this correspondence through Choi-rank-two linear combinations of Kraus operators, higher-rank relative spectra, structural obstructions, and constructions with prescribed Choi rank. We distinguish injective identification from full tomography, perfect one-shot discrimination, zero-error classical communication, and exact quantum correction. Twirling channels then provide a structured setting in which commutants, irreducible dimensions, multiplicities, orbit-frame orthogonality, coding indices, and phase-retrievable subspaces can be read from group representations.

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