Separability conditions from the Landau-Pollak uncertainty relation (8 pages)

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested and compared with previously stated criteria by applying them to states whose separability limits are already known. Our results are also extended to multipartite and higher-dimensional systems.

[1]  Horodecki Information-theoretic aspects of inseparability of mixed states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[2]  I. D. Ivonovic Geometrical description of quantal state determination , 1981 .

[3]  J. Cirac,et al.  Optimization of entanglement witnesses , 2000, quant-ph/0005014.

[4]  H. P. Robertson The Uncertainty Principle , 1929 .

[5]  Note on separability of the Werner states in arbitrary dimensions 1 This work was supported in part , 2000, quant-ph/0001110.

[6]  Jorge Sánchez,et al.  Entropic uncertainty and certainty relations for complementary observables , 1993 .

[7]  N. Gisin Hidden quantum nonlocality revealed by local filters , 1996 .

[8]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[9]  J. Schwinger UNITARY OPERATOR BASES. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[10]  D. Deutsch Uncertainty in Quantum Measurements , 1983 .

[11]  H. Hofmann,et al.  Violation of local uncertainty relations as a signature of entanglement , 2002, quant-ph/0212090.

[12]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[13]  M. Lewenstein,et al.  Separability Criteria from Uncertainty Relations , 2004, quant-ph/0409140.

[14]  Cirac,et al.  Inseparability criterion for continuous variable systems , 1999, Physical review letters.

[15]  W. Wootters,et al.  Optimal state-determination by mutually unbiased measurements , 1989 .

[16]  M. Lewenstein,et al.  Entropic uncertainty relations and entanglement , 2004, quant-ph/0403219.

[17]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[18]  States of minimal joint uncertainty for complementary observables in three-dimensional Hilbert space , 1994 .

[19]  Jorge Sánchez-Ruiz Maassen-Uffink entropic uncertainty relation for angular momentum observables , 1993 .

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

[21]  Separability conditions from entropic uncertainty relations , 2003, quant-ph/0307171.

[22]  W. Thirring,et al.  A Geometric picture of entanglement and Bell inequalities , 2001, quant-ph/0111116.

[23]  A. Peres All the Bell Inequalities , 1998, quant-ph/9807017.

[24]  O. Gühne Characterizing entanglement via uncertainty relations. , 2003, Physical review letters.

[25]  Pérès Separability Criterion for Density Matrices. , 1996, Physical review letters.

[26]  Jorge Sánchez-Ruiz Improved bounds in the entropic uncertainty and certainty relations for complementary observables , 1995 .

[27]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

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