Metric on the space of quantum states from relative entropy. Tomographic reconstruction. (English) Zbl 1373.81041
Summary: In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, \(N\) level quantum states, by means of a suitably defined coordinate free differential calculus. The cases \(N=2\), \(N=3\) are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states.
MSC:
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 94A17 | Measures of information, entropy |
| 47L07 | Convex sets and cones of operators |
| 52A10 | Convex sets in \(2\) dimensions (including convex curves) |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
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