Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states

We consider the problem of evaluating the entanglement of non-Gaussian mixed states generated by photon subtraction from entangled squeezed states. The entanglement measures we use are the negativity and the logarithmic negativity. These measures possess the unusual property of being computable with linear algebra packages even for high-dimensional quantum systems. We numerically evaluate these measures for the non-Gaussian mixed states which are generated by photon subtraction with on/off photon detectors. The results are compared with the behavior of certain operational measures, namely the teleportation fidelity and the mutual information in the dense coding scheme. It is found that all of these results are mutually consistent, in the sense that whenever the enhancement is seen in terms of the operational measures, the negativity and the logarithmic negativity are also enhanced.

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

[2]  J. Eisert,et al.  A comparison of entanglement measures , 1998, quant-ph/9807034.

[3]  Hyunchul Nha,et al.  Proposed test of quantum nonlocality for continuous variables. , 2004, Physical review letters.

[4]  M. Horodecki,et al.  The asymptotic entanglement cost of preparing a quantum state , 2000, quant-ph/0008134.

[5]  J. Preskill,et al.  Encoding a qubit in an oscillator , 2000, quant-ph/0008040.

[6]  Gershon Kurizki,et al.  Improvement on teleportation of continuous variables by photon subtraction via conditional measurement , 2000 .

[7]  F. Illuminati,et al.  Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states , 2005, quant-ph/0506124.

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

[9]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[10]  J Eisert,et al.  Distilling Gaussian states with Gaussian operations is impossible. , 2002, Physical review letters.

[11]  Loophole-free test of quantum nonlocality using high-efficiency homodyne detectors , 2004, quant-ph/0407181.

[12]  M. Plenio Logarithmic negativity: a full entanglement monotone that is not convex. , 2005, Physical review letters.

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

[14]  M. Horodecki,et al.  Limits for entanglement measures. , 1999, Physical review letters.

[15]  Vaidman Teleportation of quantum states. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[16]  G. Vidal On the characterization of entanglement , 1998 .

[17]  Samuel L. Braunstein,et al.  Dense coding for continuous variables , 1999, quant-ph/9910010.

[18]  C. Xie,et al.  Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam. , 2002, Physical review letters.

[19]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[20]  Timothy C. Ralph,et al.  Experimental investigation of continuous-variable quantum teleportation , 2002, quant-ph/0207179.

[21]  Xiaolong Su,et al.  Experimental demonstration of unconditional entanglement swapping for continuous variables. , 2004, Physical review letters.

[22]  A. Furusawa,et al.  High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables. , 2005, Physical review letters.

[23]  Masashi Ban LETTER TO THE EDITOR: Quantum dense coding via a two-mode squeezed-vacuum state , 1999 .

[24]  J. Cirac,et al.  Characterization of Gaussian operations and distillation of Gaussian states , 2002, quant-ph/0204085.

[25]  N J Cerf,et al.  Proposal for a loophole-free Bell test using homodyne detection. , 2004, Physical review letters.

[26]  Enhancement of nonlocality in phase space , 2004 .

[27]  Gerard J. Milburn,et al.  Teleportation improvement by conditional measurements on the two-mode squeezed vacuum , 2002 .

[28]  Matteo G. A. Paris,et al.  Teleportation improvement by inconclusive photon subtraction , 2003 .

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

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

[31]  J. Fiurášek Gaussian transformations and distillation of entangled Gaussian states. , 2002, Physical review letters.

[32]  W. Munro,et al.  A near deterministic linear optical CNOT gate , 2004 .

[33]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[34]  Masahide Sasaki,et al.  Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state , 2005 .

[35]  J. Eisert,et al.  Driving non-Gaussian to Gaussian states with linear optics , 2003 .

[36]  H. Kimble,et al.  Teleportation of continuous quantum variables , 1998, Technical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236).

[37]  H. J. Kimble,et al.  Quantum teleportation of light beams , 2003 .