Local versus nonlocal information in quantum-information theory: Formalism and phenomena
By Michal Horodecki, Pawel Horodecki, Ryszard Horodecki, Jonathan Oppenheim, A. S. De, Ujjwal Sen, Barbara Synak. 2004
371 citations recorded by the source corpus.
In spite of many results in quantum information theory, the complex nature of compound systems is far from clear. In general the information is a mixture of local and nonlocal ('quantum') information. It is important from both pragmatic and theoretical points of view to know the relationships between the two components. To make this point more clear, we develop and investigate the quantum-information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudoclassically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal - i.e., has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other nonlocal phenomena which can be found using themore » paradigm of local information. For example, we prove the existence of a form of nonlocality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal. We also show that there do not exist states for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proved that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.« less
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Citations in the corpus
- Partial quantum information (2005, unknown): “Secondly, the measurement of Alice makes her state completely product with R , thus reinforcing the interpretation of quantum mutual information as the minimum entropy production of any local decorrelating process 14,15 .”
- Quantum coherence and geometric quantum discord (2017, background): “They discussed the protocol of quantum state merging under IO, which they called incoherent quantum state merging, and is indeed an analog of the standard state merging with general quantum operations (Horodecki et al., 2005b).”
- Quantum resource theories (2018, background): “The latter provided one of the first explicit constructions of a QRT that is different than entanglement theory, although the framework for a QRT of information had already been investigated in a series of earlier papers (Horodecki et al., 2003a, 2005b; Oppenheim et al., 2002).”
- The classical-quantum boundary for correlations: Discord and related measures (2011, background): “The discords for a measurement on A are D(B|A) = 0.05, Dth(B|A) = 0.20, D(B|{ΠEiga }) = 0.21, (49) and the discords for a measurement on B are zero.”
- Quantum, classical, and total amount of correlations in a quantum state (2004, background): “It has been suggested [20, 21] that the (regularised) relative entropy of entanglement should relate to the entanglement erasure — while this would be a most interesting result, we see no clear evidence either way.”