Entanglement of formation for symmetric Gaussian states.

We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems.

[1]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[2]  R. Schnabel,et al.  Experimental demonstration of continuous variable polarization entanglement. , 2002, Physical review letters.

[3]  B. Julsgaard,et al.  Experimental long-lived entanglement of two macroscopic objects , 2001, Nature.

[4]  J. Cirac,et al.  Entanglement criteria for all bipartite Gaussian states. , 2001, Physical review letters.

[5]  R. Werner,et al.  Entanglement measures under symmetry , 2000, quant-ph/0010095.

[6]  M. Wolf,et al.  Bound entangled Gaussian states. , 2000, Physical review letters.

[7]  William K. Wootters,et al.  Entanglement of formation and concurrence , 2001, Quantum Inf. Comput..

[8]  Michal Horodecki,et al.  Entanglement measures , 2001, Quantum Inf. Comput..

[9]  Pawel Horodecki,et al.  Distillation and bound entanglement , 2001, Quantum Inf. Comput..

[10]  K. Vollbrecht,et al.  Entanglement of formation for isotropic states , 2000, Physical review letters.

[11]  Simón.  Peres-horodecki separability criterion for continuous variable systems , 1999, Physical review letters.

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

[13]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

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

[15]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

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