Correlative capacity of composite quantum states.

We characterize the optimal correlative capacity of entangled, separable, and classically correlated states. Introducing the notions of the infimum and supremum within majorization theory, we construct the least disordered separable state compatible with a set of marginals. The maximum separable correlation information supportable by the marginals of a multiqubit pure state is shown to be a local operations and classical communication monotone. The least disordered composite of a pair of qubits is found for the above classes, with classically correlated states defined as diagonal in the product of marginal bases.

[1]  M. Nielsen.  Conditions for a Class of Entanglement Transformations , 1998, quant-ph/9811053.

[2]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[3]  Michael M. Wolf,et al.  Bell inequalities and entanglement , 2001, Quantum Inf. Comput..

[4]  V. Vedral,et al.  Classical, quantum and total correlations , 2001, quant-ph/0105028.

[5]  M. Nielsen.  Probability distributions consistent with a mixed state , 1999, quant-ph/9909020.

[6]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.

[7]  M. Partovi,et al.  Entanglement versus Stosszahlansatz: disappearance of the thermodynamic arrow in a high-correlation environment. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[9]  Animesh Datta,et al.  Signatures of nonclassicality in mixed-state quantum computation , 2008, 0811.4003.

[10]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[11]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[12]  Charles H. Bennett,et al.  Exact and asymptotic measures of multipartite pure-state entanglement , 1999, Physical Review A.

[13]  A. Sudbery,et al.  One-qubit reduced states of a pure many-qubit state: polygon inequalities. , 2002, Physical review letters.

[14]  E. Schrödinger.  Discussion of Probability Relations between Separated Systems , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  M. Nielsen,et al.  Interdisciplinary Physics: Biological Physics, Quantum Information, etc. , 2001 .

[16]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

[17]  W. Zurek,et al.  Quantum discord: a measure of the quantumness of correlations. , 2001, Physical review letters.

[18]  B. Lanyon,et al.  Experimental quantum computing without entanglement. , 2008, Physical review letters.

[19]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[20]  M. Nielsen,et al.  Separable states are more disordered globally than locally. , 2000, Physical review letters.