A new class of entanglement measures. (English) Zbl 1018.81006
Summary: We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.
MSC:
81P68 | Quantum computation |
81P15 | Quantum measurement theory, state operations, state preparations |
Keywords:
greatest cross norm; satisfy the basic requirements; local unitary operations; local quantum operations and classical communicationReferences:
[1] | Rudolph O., J. Phys. A 33 pp 3951– (2000) · Zbl 0947.46054 · doi:10.1088/0305-4470/33/21/308 |
[2] | Bennett C. H., Phys. Rev. A 54 pp 3824– (1997) · Zbl 1371.81041 · doi:10.1103/PhysRevA.54.3824 |
[3] | Vedral V., Phys. Rev. Lett. 78 pp 2275– (1997) · Zbl 0944.81011 · doi:10.1103/PhysRevLett.78.2275 |
[4] | Vedral V., Phys. Rev. A 57 pp 1619– (1998) · doi:10.1103/PhysRevA.57.1619 |
[5] | Plenio M. B., Contemp. Phys. 39 pp 431– (1998) · doi:10.1080/001075198181766 |
[6] | Horodecki M., Phys. Rev. Lett. 84 pp 2014– (2000) · doi:10.1103/PhysRevLett.84.2014 |
[7] | DOI: 10.1080/09500340008244048 · doi:10.1080/09500340008244048 |
[8] | Horodecki M., Phys. Rev. Lett. 80 pp 5239– (1998) · Zbl 0947.81005 · doi:10.1103/PhysRevLett.80.5239 |
[9] | Bennett C. H., Phys. Rev. Lett. 82 pp 5385– (1999) · doi:10.1103/PhysRevLett.82.5385 |
[10] | Rudolph O., J. Math. Phys. 42 pp 2507– (2001) · Zbl 1016.81009 · doi:10.1063/1.1370954 |
[11] | DOI: 10.1016/0003-4916(71)90108-4 · Zbl 1229.81137 · doi:10.1016/0003-4916(71)90108-4 |
[12] | M. J. Donald, M. Horodecki, and O. Rudolph, The uniqueness theorem for entanglement measures, quant-ph/0105017. |
[13] | DOI: 10.1016/0024-3795(75)90075-0 · Zbl 0327.15018 · doi:10.1016/0024-3795(75)90075-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.