2023/11/27 by Kai Liu, Liu, Kai, Deguang Han +1 · 2 citations
Computer Science · Engineering · #Advancements in Photolithography Techniques #Blind Source Separation Techniques #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2311.16359
openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A phase retrievable quantum channel refers to a quantum channel Φ: B(HA)→ B(HB) such that there is a positive operator valued measure (POVM) \Fj\ in B(HB) and \Φ^*(Fj)\ is a phase retrievable operator valued frame. In this paper we examine the phase retrievable quantum channels in terms of their Kraus representations. For quantum channels Φ of Choi's rank-2, we obtain a necessary and sufficient condition under which it is phase retrievable. For the general case, we present several necessary and/or sufficient conditions. In particular, a necessary and sufficient condition is obtained in terms of the relevant matrix-valued joint spectrum of the Kraus operators. Additionally, we also examine, by examples, the problem of constructing quantum channels such that there exists a minimal number of rank-one observables \Fj\ such that \Φ^*(Fj)\ does phase retrieval for HA. Conversely, for a given set of rank-one observables \Fj\j=1N, we present a sufficient condition under which, for every 1≤ r≤ N given, a phase retrievable quantum channel Φ of Choi's rank-r can be explicitly constructed.