Secure coherent-state quantum key distribution protocols with efficient reconciliation

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

[1]  Frédéric Grosshans.  Collective attacks and unconditional security in continuous variable quantum key distribution. , 2005, Physical review letters.

[2]  T. Ralph,et al.  Continuous variable quantum cryptography , 1999, quant-ph/9907073.

[3]  Nicolas J. Cerf,et al.  Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables , 2003, Quantum Inf. Comput..

[4]  P. Navez,et al.  Statistical confidentiality tests for a quantum transmission using continuous variables , 2002 .

[5]  I Devetak,et al.  Relating quantum privacy and quantum coherence: an operational approach. , 2004, Physical review letters.

[6]  G. M. D'Ariano,et al.  Systematic and statistical errors in homodyne measurements of the density matrix , 1997 .

[7]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[8]  M. Hillery.  Quantum cryptography with squeezed states , 1999, quant-ph/9909006.

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

[10]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[11]  G Leuchs,et al.  Continuous variable quantum cryptography: beating the 3 dB loss limit. , 2002, Physical review letters.

[12]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[13]  Jean Cardinal,et al.  Reconciliation of a quantum-distributed Gaussian key , 2001, IEEE Transactions on Information Theory.

[14]  H. Yuen,et al.  Secure communication using mesoscopic coherent states. , 2002, Physical review letters.

[15]  A. Steane.  Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  Frédéric Grosshans,et al.  Continuous-variable quantum cryptography is secure against non-Gaussian attacks. , 2004, Physical review letters.

[17]  Gerd Leuchs,et al.  Continuous-variable quantum key distribution using polarization encoding and post selection , 2004, quant-ph/0403064.

[18]  A. Acín,et al.  Security bounds for continuous variables quantum key distribution. , 2004, Physical review letters.

[19]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[20]  G Leuchs,et al.  Quantum key distribution with bright entangled beams. , 2002, Physical review letters.

[21]  John Preskill,et al.  Secure quantum key distribution using squeezed states , 2001 .

[22]  N. Cerf,et al.  Quantum distribution of Gaussian keys using squeezed states , 2000, quant-ph/0008058.

[23]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.

[24]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[25]  N J Cerf,et al.  Security of quantum key distribution with coherent states and homodyne detection. , 2004, Physical review letters.

[26]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[27]  Shor,et al.  Simple proof of security of the BB84 quantum key distribution protocol , 2000, Physical review letters.

[28]  M. Reid.  Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations , 1999, quant-ph/9909030.