Academic Journal
Phase retrievability of frames and quantum channels
| Τίτλος: | Phase retrievability of frames and quantum channels |
|---|---|
| Συγγραφείς: | Liu, Kai, Han, Deguang |
| Πηγή: | Linear Algebra and its Applications. 725:378-400 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Elsevier BV, 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | Quantum Physics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Mathematical Physics |
| Περιγραφή: | A phase retrievable quantum channel refers to a quantum channel $Φ: B(H_A)\to B(H_B)$ such that there is a positive operator valued measure (POVM) $\{F_{j}\}$ in $B(H_{B})$ and $\{Φ^*(F_j)\}$ 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 $\{F_{j}\}$ such that $\{Φ^*(F_j)\}$ does phase retrieval for $H_A$. Conversely, for a given set of rank-one observables $\{F_{j}\}_{j=1}^{N}$, we present a sufficient condition under which, for every $1\leq r\leq N$ given, a phase retrievable quantum channel $Φ$ of Choi's rank-$r$ can be explicitly constructed. |
| Τύπος εγγράφου: | Article |
| Γλώσσα: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.07.014 |
| DOI: | 10.48550/arxiv.2311.16359 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2311.16359 |
| Rights: | Elsevier TDM CC BY NC ND |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....a517a7e54ec74d585037a3c62f3cdefb |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 00243795 |
|---|---|
| DOI: | 10.1016/j.laa.2025.07.014 |