This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages)
|
In quantum information and quantum computation, an entanglement monotone or entanglement measure is a function that quantifies the amount of entanglement present in a quantum state. Any entanglement monotone is a nonnegative function whose value does not increase under local operations and classical communication.[1][2]
Definition
editLet be the space of all states, i.e., Hermitian positive semi-definite operators with trace one, over the bipartite Hilbert space . An entanglement measure is a function such that:
- if is separable;
- Monotonically decreasing under LOCC, viz., for the Kraus operator corresponding to the LOCC , let and for a given state , then (i) does not increase under the average over all outcomes, and (ii) does not increase if the outcomes are all discarded, .
Some authors also add the condition that over the maximally entangled state . If the nonnegative function only satisfies condition 2 of the above, then it is called an entanglement monotone.
Various entanglement monotones exist for bipartite systems as well as for multipartite systems. Common entanglement monotones are the entropy of entanglement, concurrence, negativity, squashed entanglement, entanglement of formation and tangle.
References
edit- ^ Horodecki, Ryszard; Horodecki, Paweł; Horodecki, Michał; Horodecki, Karol (2009-06-17). "Quantum entanglement". Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. S2CID 59577352.
- ^ Chitambar, Eric; Gour, Gilad (2019-04-04). "Quantum resource theories". Reviews of Modern Physics. 91 (2): 025001. arXiv:1806.06107. Bibcode:2019RvMP...91b5001C. doi:10.1103/RevModPhys.91.025001. S2CID 119194947.