Quantum teleportation with continuous variables: A survey

Very recently, we took part in a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development is mainly due to the experimental and theoretical advantages offered by CV systems, i.e., quantum systems described by a set of observables, like position and momentum, which have a continuous spectrum of eigenvalues. According to this novel trend, quantum information protocols like quantum teleportation have been suitably extended to the CV framework. Here, we briefly review some mathematical tools relative to CV systems, and we consequently develop the concepts of quantum entanglement and teleportation in the CV framework by analogy with the qubit-based approach. Some connections between teleportation fidelity and entanglement properties of the underlying quantum channel are inspected. Next, we address the study of CV quantum teleportation networks where more users share a multipartite state and an arbitrary pair of them performs quantum teleportation. In this context, we show alternative protocols, and we investigate the optimal strategy that maximizes the performance of the network.

[1]  A. Holevo,et al.  Capacity of quantum Gaussian channels , 1999 .

[2]  J. Eisert,et al.  Introduction to the basics of entanglement theory in continuous-variable systems , 2003, quant-ph/0312071.

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

[4]  Alessio Serafini,et al.  LETTER TO THE EDITOR: Symplectic invariants, entropic measures and correlations of Gaussian states , 2003, quant-ph/0307073.

[5]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[6]  Jaromir Fiurasek.  Improving the fidelity of continuous-variable teleportation via local operations , 2002 .

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

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

[9]  Stefano Mancini,et al.  Light reflection upon a movable mirror as a paradigm for continuous variable teleportation network , 2004 .

[10]  Stefano Mancini,et al.  Erratum: Conditioning two-party quantum teleportation within a three-party quantum channel [Phys. Rev. A 71, 042326 (2005)] , 2005 .

[11]  Samuel L. Braunstein,et al.  Quantum error correction for communication with linear optics , 1998, Nature.

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

[13]  J I Cirac,et al.  Entanglement versus correlations in spin systems. , 2004, Physical review letters.

[14]  Samuel L. Braunstein,et al.  Criteria for continuous-variable quantum teleportation , 1999, quant-ph/9910030.

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

[16]  C. Xie,et al.  Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables. , 2002, Physical review letters.

[17]  L. Knoll,et al.  Continuous-variable quantum teleportation through lossy channels , 2002 .

[18]  Braunstein,et al.  Multipartite entanglement for continuous variables: A quantum teleportation network , 1999, Physical review letters.

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

[20]  Stefano Mancini,et al.  Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure , 2003 .

[21]  F. Illuminati,et al.  Equivalence between entanglement and the optimal fidelity of continuous variable teleportation. , 2004, Physical review letters.

[22]  N. Lutkenhaus,et al.  Bell measurements for teleportation , 1998, quant-ph/9809063.

[23]  Ipe,et al.  Cloning of continuous quantum variables , 1999, Physical review letters.

[24]  Stefano Pirandola.  A QUANTUM TELEPORTATION GAME , 2005 .

[25]  W. Bowen,et al.  Tripartite quantum state sharing. , 2003, Physical review letters.

[26]  Stefano Mancini,et al.  Conditioning two-party quantum teleportation within a three-party quantum channel , 2005 .

[27]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

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

[29]  Gerardo Adesso,et al.  Unitarily localizable entanglement of gaussian states , 2005 .

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

[31]  G. D’Ariano,et al.  Bell measurements and observables , 2000, quant-ph/0005121.

[32]  M. G. A. Paris,et al.  Three-mode entanglement by interlinked nonlinear interactions in optical χ (2) media , 2004 .

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

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

[35]  Sudarshan,et al.  Gaussian-Wigner distributions in quantum mechanics and optics. , 1987, Physical review. A, General physics.

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

[38]  F. Illuminati,et al.  Extremal entanglement and mixedness in continuous variable systems , 2004, quant-ph/0402124.

[39]  Stefano Mancini,et al.  Scheme for teleportation of quantum states onto a mechanical resonator. , 2003, Physical review letters.

[40]  Samuel L. Braunstein,et al.  Quantum versus classical domains for teleportation with continuous variables , 2001 .

[41]  J. Williamson.  On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems , 1936 .

[42]  M. Horodecki,et al.  Teleportation, Bell's inequalities and inseparability , 1996, quant-ph/9606027.

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

[44]  Hidehiro Yonezawa,et al.  Experimental creation of a fully inseparable tripartite continuous-variable state. , 2003, Physical review letters.

[45]  P. van Loock,et al.  Quantum Communication with Continuous Variables , 2002 .

[46]  A. Furusawa,et al.  Demonstration of a quantum teleportation network for continuous variables , 2004, Nature.