Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel

We present two error-tolerance transmission protocols of a single-photon polarization state when bit-flip error is taken into account. For achieving the transmission target of the single-photon state, the first protocol needs to encode it to a nonmaximally entangled Bell state. Exploiting the interaction of the polarization entanglement with spatial entanglement between two photons, its success probability is 100 %. Different from the first protocol, the second one utilizes the idea of teleportation with an auxiliary Bell state. By performing quantum nondemolition measurement to analyze the parity, conventional measurement, and unitary transformation operations, the success probability of the second protocol is approximately unity. Furthermore, the second protocol can be generalized to the error-tolerance transmission of an arbitrary mixed state or the distribution of an arbitrary multi-photon entangled state.

[1]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[2]  B. He,et al.  Continuous-mode effects and photon-photon phase gate performance , 2010, 1012.1683.

[3]  Shengmei Zhao,et al.  Efficient entanglement concentration for arbitrary less-entangled NOON states , 2012, Quantum Information Processing.

[4]  Laflamme,et al.  Perfect Quantum Error Correcting Code. , 1996, Physical review letters.

[5]  Barry C. Sanders,et al.  Entanglement creation with negative index metamaterials , 2012, 1205.4506.

[6]  Jian Li,et al.  Quantum control gates with weak cross-Kerr nonlinearity , 2008, 0811.3364.

[7]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[8]  H. Weinfurter,et al.  Multiphoton entanglement and interferometry , 2003, 0805.2853.

[9]  Fuguo Deng.  One-step error correction for multipartite polarization entanglement , 2011, 1107.0093.

[10]  Li Dong,et al.  A nearly deterministic scheme for generating χ-type entangled states with weak cross-Kerr nonlinearities , 2013, Quantum Inf. Process..

[11]  Yu-Bo Sheng,et al.  Efficient quantum entanglement distribution over an arbitrary collective-noise channel , 2010, 1005.0050.

[12]  D. Bouwmeester,et al.  Bit-flip-error rejection in optical quantum communication , 2001 .

[13]  R. Laflamme,et al.  Robust polarization-based quantum key distribution over a collective-noise channel. , 2003, Physical review letters.

[14]  E. Knill.  Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics , 2003, quant-ph/0307015.

[15]  Jeffrey H. Shapiro,et al.  Continuous-time cross-phase modulation and quantum computation , 2007 .

[16]  Li Dong,et al.  Nearly deterministic controlled-not gate with weak cross-kerr nonlinearities , 2012, Quantum Inf. Comput..

[17]  Demetrios A. Kalamidas.  Single-photon quantum error rejection and correction with linear optics , 2005, quant-ph/0506114.

[18]  Li Dong,et al.  Construction scheme of a two-photon polarization controlled arbitrary phase gate mediated by weak cross-phase modulation , 2013 .

[19]  Xiang-bin Wang.  Quantum error-rejection code with spontaneous parametric down-conversion (7 pages) , 2004 .

[20]  Barry C Sanders,et al.  Large cross-phase modulation between slow copropagating weak pulses in 87Rb. , 2006, Physical review letters.

[21]  P. Zanardi,et al.  Noiseless Quantum Codes , 1997, quant-ph/9705044.

[22]  Lan Zhou,et al.  Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications , 2013, Entropy.

[23]  Gilles Nogues,et al.  Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED , 1999 .

[24]  Hood,et al.  Measurement of conditional phase shifts for quantum logic. , 1995, Physical review letters.

[25]  Fuguo Deng,et al.  Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics , 2008, 0806.0115.

[26]  B. He,et al.  Transverse multimode effects on the performance of photon-photon gates , 2010, 1006.3584.

[27]  Xin-Wen Wang,et al.  Nondestructive two-photon parity detector with near unity efficiency , 2013 .

[28]  Shi-Qing Tang,et al.  Photonic two-qubit parity gate with tiny cross–Kerr nonlinearity , 2011, 1112.6135.

[29]  Yu-Bo Sheng,et al.  Hybrid entanglement purification for quantum repeaters , 2013 .

[30]  Demetrios Kalamidas.  Feasible quantum error detection with linear optics , 2004 .

[31]  Lan Zhou,et al.  Efficient entanglement concentration for arbitrary single-photon multimode W state , 2012, 1210.6178.

[32]  Xihan Li.  Deterministic polarization-entanglement purification using spatial entanglement , 2010, 1010.5301.

[33]  Jie Song,et al.  Effective protocol for preparation of four-photon polarization-entangled decoherence-free states with cross-Kerr nonlinearity , 2013 .

[34]  Li Dong,et al.  Two-party quantum privacy comparison with polarization-entangled bell states and the coherent states , 2014, Quantum Inf. Comput..

[35]  Yu-Guang Yang,et al.  Fault-tolerant quantum secret sharing against collective noise , 2011 .

[36]  Ite A. Yu,et al.  Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels , 2011 .

[37]  Kae Nemoto,et al.  Weak nonlinearities: a new route to optical quantum computation , 2005, quant-ph/0507084.

[38]  Yu-Bo Sheng,et al.  Efficient faithful qubit transmission with frequency degree of freedom , 2009, 0907.0053.

[39]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[40]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[41]  Jeffrey H. Shapiro,et al.  Single-photon Kerr nonlinearities do not help quantum computation , 2006 .

[42]  Xi-Han Li,et al.  Efficient quantum key distribution over a collective noise channel (6 pages) , 2008, 0808.0042.

[43]  Fuguo Deng,et al.  Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity , 2008, 0805.0032.

[44]  Julio Gea-Banacloche,et al.  Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets , 2009, 0911.4682.

[45]  B. Zheng,et al.  Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs , 2012, 1202.2190.

[46]  Hong-Yu Zhou,et al.  Passively self-error-rejecting qubit transmission over a collective-noise channel , 2008, Quantum Inf. Comput..

[47]  J. D. Franson,et al.  Probabilistic quantum logic operations using polarizing beam splitters , 2001, quant-ph/0107091.

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

[49]  Qi Guo,et al.  Simplified optical quantum-information processing via weak cross-Kerr nonlinearities , 2011 .

[50]  Bing He,et al.  Single-photon logic gates using minimal resources , 2009, 0909.0300.

[51]  X. Yi,et al.  Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel , 2011 .

[52]  T. Spiller,et al.  Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities , 2004, quant-ph/0408117.

[53]  Xiang‐Bin Wang.  Fault tolerant quantum key distribution protocol with collective random unitary noise , 2005 .

[54]  J. Marangos,et al.  Electromagnetically induced transparency : Optics in coherent media , 2005 .

[55]  Aephraim M. Steinberg,et al.  Amplifying single-photon nonlinearity using weak measurements. , 2010, Physical review letters.

[56]  Shengmei Zhao,et al.  Efficient two-step entanglement concentration for arbitrary W states , 2012, 1202.3019.

[57]  Fuguo Deng,et al.  Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement , 2010 .

[58]  Chang-Yi Wang,et al.  Low-light-level cross-phase-modulation based on stored light pulses. , 2006, Physical review letters.

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

[60]  Masato Koashi,et al.  Probabilistic manipulation of entangled photons , 2001 .

[61]  Shahram Mohammad Nejad,et al.  An error-free protocol for quantum entanglement distribution in long-distance quantum communication , 2011, 2010 7th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP 2010).

[62]  N Imoto,et al.  Faithful qubit distribution assisted by one additional qubit against collective noise. , 2005, Physical review letters.

[63]  Christoph Simon,et al.  Cross-Kerr nonlinearity between continuous-mode coherent states and single photons , 2011, 1102.3724.

[64]  R. G. Beausoleil,et al.  High-efficiency quantum-nondemolition single-photon-number-resolving detector , 2005 .

[65]  Io-Chun Hoi,et al.  Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. , 2012, Physical review letters.

[66]  M. J. Fitch,et al.  Experimental controlled-NOT logic gate for single photons in the coincidence basis , 2003, quant-ph/0303095.

[67]  L Aolita,et al.  Quantum communication without alignment using multiple-qubit single-photon states. , 2007, Physical review letters.

[68]  Xin-Wen Wang,et al.  Nondestructive Greenberger-Horne-Zeilinger-state analyzer , 2013, Quantum Inf. Process..

[69]  Bing He,et al.  Universal entangler with photon pairs in arbitrary states , 2008, 0806.4216.

[70]  E. Andersson,et al.  Experimentally realizable quantum comparison of coherent states and its applications , 2006, quant-ph/0601130.

[71]  Bing He,et al.  Creation of high-quality long-distance entanglement with flexible resources , 2008, 0808.2320.

[72]  Li Dong,et al.  Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules , 2013 .

[73]  Fuguo Deng,et al.  Faithful qubit transmission against collective noise without ancillary qubits , 2007, 0708.0068.

[74]  Li Dong,et al.  Quantum key distribution with Einstein–Podolsky–Rosen pairs associated with weak cross-Kerr nonlinearities , 2012 .

[75]  Bing He,et al.  Efficient generation of universal two-dimensional cluster states with hybrid systems , 2010, 1005.1112.