Entanglement monotone


In quantum information and quantum computation, an entanglement monotone 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

Let 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:

  1. if is separable;
  2. 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.

References

  1. 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.
  2. 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.
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