Volume of the set of LOCC-convertible quantum states
| Autor: | Fabio Deelan Cunden, Paolo Facchi, Giuseppe Florio, Giovanni Gramegna |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Wishart distribution Pure mathematics General Physics and Astronomy FOS: Physical sciences Quantum entanglement 01 natural sciences random matrices 010305 fluids & plasmas Entanglement local operations and classical communication majorization Quantum state 0103 physical sciences FOS: Mathematics Limit (mathematics) 010306 general physics Mathematical Physics Mathematics LOCC Quantum Physics Stochastic process Probability (math.PR) Statistical and Nonlinear Physics Mathematical Physics (math-ph) Scaling limit Modeling and Simulation Quantum Physics (quant-ph) Random matrix Mathematics - Probability |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical |
| ISSN: | 1751-8113 1533-7146 0305-4470 1742-5468 |
| DOI: | 10.1088/1751-8121/ab7b21 |
| Popis: | The class of quantum operations known as Local Operations and Classical Communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to the unitarily invariant measure) of the set of LOCC-convertible bipartite pure states, where the ordering is characterised by an algebraic relation known as majorization. The numerical results, which exploit a tridiagonal model of random matrices, provide quantitative evidence that the proportion of LOCC-convertible pairs vanishes in the limit of large dimension, and therefore support a previous conjecture by Nielsen. In particular, we show that the problem is equivalent to the persistence of a non-Markovian stochastic process and the proportion of LOCC-convertible pairs decays algebraically with a nontrivial persistence exponent. We extend this analysis by investigating the distribution of the maximal success probability of LOCC-conversions. We show a dichotomy in behaviour between balanced and unbalanced bipartitions. In the latter case the asymptotics is somehow surprising: in the limit of large dimensions, for the overwhelming majority of pairs of states a perfect LOCC-conversion is not possible; nevertheless, for most states there exist local strategies that succeed in achieving the conversion with a probability arbitrarily close to one. We present strong evidences of a universal scaling limit for the maximal probability of successful LOCC-conversions and we suggest a connection with the typical fluctuations of the smallest eigenvalue of Wishart random matrices. 29 pages, 8 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|