Concentrating entanglement by local actions: Beyond mean values

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 63, Issue 2, 2001, Pages 022301-022301

  Lo, Hoi Kwong ^a   Popescu, Sandu ^b,c  

^a MagiQ Technologies Inc   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c HEWLETT PACKARD LABORATORIES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

SCHMIDT DECOMPOSITION;

COMMUNICATION; ELECTRON ENERGY LEVELS; MEASUREMENT THEORY; PROBABILITY DISTRIBUTIONS;

QUANTUM THEORY;

EID: 14344280810     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.63.022301     Document Type: Article

References (26)

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19. This equivalence (or invariance) between the outcomes of Alice and Bob's local experiments is easy to understand in the case where Alice and Bob share no initial entanglement. In this case, consider, for instance, Bob prepares a spin-1/2 object in his own laboratory along the z axis and then measures its spin along the x axis. The outcome of this simple experiment is, of course, equally probable to be up or down. Such an experiment by Bob can be mapped into an experiment by Alice in which she prepares a spin-1/2 object in her own laboratory along the z axis, and then measures its spin along the x axis. Just like Bob's experiment, Alice's experiment also gives equiprobable outcomes. In this sense, the two experiments are equivalent. On the contrary, suppose that Alice, but not Bob, shares some initial entanglement with Charles. Alice can then teleport states to and from with Charles, whereas Bob cannot. It is then clear that Alice's local experiments (plus classical communications) are not generally equivalent to those of Bob. In conclusion, entanglement with a third party generally destroys the equivalence of local experiments between two observers. In this paper, we show, however, that two persons, Alice and Bob, sharing a pure entangled initial state still respect the equivalence in local experiments. This observation, which greatly simplifies our analysis, is not a priori obvious. Note that this equivalence is used here to prove that two-way communications can be reduced to one-way communications in the context of entanglement manipulations of a pure entangled state. Curiously, another equivalence (symmetry) argument was previously used to prove that two-way communications is provably better than one-way communications in entanglement purification of mixed states [7]. In our opinion, the power of symmetry arguments in entanglement manipulations remains to be fully explored.
20. We use the superscript MAX because, as shown in Sec. V, the supremum probability is attainable by the optimal strategy.
21. This lemma was also proven by other groups such as by C. H. Bennett and J. Smolin (private communications) and M. Nielson (private communications). We thank them for helpful discussions.
22. This lemma was also proven by other groups such as by C. H. Bennett and J. Smolin (private communications) and M. Nielson (private communications). We thank them for helpful discussions.
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25. It is an interesting open question whether there exists any mixed state that respects an interchange symmetry between Alice and Bob for all strategies of entanglement manipulations. We thank M. A. Nielson for raising this question.
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