Decomposition of bipartite states with applications to quantum no-broadcasting theorems

Journal Article · Thu Jul 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012338· OSTI ID:21442901

Shunlong, Luo ^[1]; Wei, Sun ^[1]

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1. Department of Mathematics and Statistics, Concordia University, H3G 1M8 Montreal, Quebec (Canada)

Correlations in bipartite quantum states are fundamental objects in quantum information theory. A canonical framework for studying correlations is the entangled versus separable dichotomy in which the decompositions of separable states as convex combinations of product states play an instrumental role. In this paper, motivated by both the representation of separable states and quantum no-broadcasting considerations, we establish a constructive decomposition representation for any bipartite state. As applications, we prove the conjectures proposed by Luo [Lett. Math. Phys. 92, 143 (2010)] concerning no-unilocal broadcasting for quantum correlations and further provide a unified picture for the celebrated quantum no-broadcasting theorem for noncommuting states by Barnum et al. [Phys. Rev. Lett. 76, 2818 (1996)], and the elegant no-local-broadcasting theorem for quantum correlations by Piani et al. [Phys. Rev. Lett. 100, 090502 (2008)]. The results reveal some intrinsic relation between quantumness of correlations and noncommutativity of states, and in particular, provide a characterization for zero quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett. 88, 017901 (2001)] from the broadcasting perspective. Furthermore, it is indicated that the distinction between the decomposition for general bipartite states and that for separable states might be useful in studying entanglement versus separability.

• OSTI ID: 21442901
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 82; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATIONS
ENERGY LEVELS
INFORMATION
MECHANICS
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM MECHANICS
QUANTUM STATES