Two-particle spin states and generalized Bell’s inequalities

A new formalism for calculation of the spin correlation magnitude is developed. In this approach, the mean value of an operator acting in the four-dimensional space of two-particle spin states has the form of a scalar product of vectors defined in the three-dimensional direction space. A complete description of the two-particle spin states satisfying Bell inequalities is given in this formalism. It is shown that these states include both factorable and entangled states.

[1]  V. Andreev,et al.  Quantum tomography of spin states and the Einstein-Podolsky-Rosen paradox , 2000 .

[2]  Robert Garisto,et al.  Entanglement of projection and a new class of quantum erasers , 1999 .

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

[4]  N. Bohr.  II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

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

[6]  M. Horodecki,et al.  Inseparable Two Spin- 1 2 Density Matrices Can Be Distilled to a Singlet Form , 1997 .

[7]  Experimental study of a subsystem in an entangled two-photon state , 1998, quant-ph/9811060.

[8]  Arno R Bohm,et al.  Quantum Mechanics: Foundations and Applications , 1993 .

[9]  T. F. Jordan.  Quantum correlations violate Einstein-Podolsky-Rosen assumptions , 1999 .

[10]  Popescu,et al.  Bell's inequalities versus teleportation: What is nonlocality? , 1994, Physical review letters.

[11]  Ryszard Horodecki,et al.  Entanglement processing and statistical inference: The Jaynes principle can produce fake entanglement , 1999 .

[12]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[13]  M. Horodecki,et al.  Quantum α-entropy inequalities: independent condition for local realism? , 1996 .

[14]  Vladimir I. Man’ko,et al.  Positive distribution description for spin states , 1997 .

[15]  M. Lewenstein,et al.  Separability and entanglement of composite quantum systems , 1997, quant-ph/9707043.