Purification of Logic-Qubit Entanglement

Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network.

[1]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[2]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

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

[4]  Deutsch,et al.  Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels. , 1996, Physical review letters.

[5]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[6]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[7]  J. Cirac,et al.  Quantum repeaters based on entanglement purification , 1998, quant-ph/9808065.

[8]  Jian-Wei Pan,et al.  Entanglement purification for quantum communication , 2000, Nature.

[9]  G. Long,et al.  Theoretically efficient high-capacity quantum-key-distribution scheme , 2000, quant-ph/0012056.

[10]  Jian-Wei Pan,et al.  Polarization entanglement purification using spatial entanglement. , 2001, Physical review letters.

[11]  M. A. Martin-Delgado,et al.  Single-Step Distillation Protocol with Generalized Beam Splitters , 2003 .

[12]  Fuguo Deng,et al.  Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block , 2003, quant-ph/0308173.

[13]  C. Beenakker,et al.  Charge detection enables free-electron quantum computation. , 2004, Physical Review Letters.

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

[15]  H. Bombin,et al.  Entanglement distillation protocols and number theory , 2005, quant-ph/0503013.

[16]  Zhuo-Liang Cao,et al.  Entanglement purification for arbitrary unknown ionic states via linear optics , 2005 .

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

[18]  Yu-Bo Sheng,et al.  Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement , 2009, 0912.0079.

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

[20]  Fuguo Deng,et al.  One-step deterministic polarization-entanglement purification using spatial entanglement , 2010, 1008.3509.

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

[22]  Zhang Yong Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities , 2011 .

[23]  W Dür,et al.  Stable macroscopic quantum superpositions. , 2011, Physical review letters.

[24]  Fu-Guo Deng,et al.  Efficient multipartite entanglement purification with the entanglement link from a subspace , 2011, 1110.0059.

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

[26]  Ru Zhang,et al.  Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system. , 2011, Optics express.

[27]  Peter van Loock,et al.  Dynamical entanglement purification using chains of atoms and optical cavities , 2011 .

[28]  Wolfgang Dür,et al.  Stability of encoded macroscopic quantum superpositions , 2012 .

[29]  P. Loock,et al.  High-fidelity entanglement purification using chains of atoms and optical cavities , 2012, 1207.6008.

[30]  W Dür,et al.  Universal and optimal error thresholds for measurement-based entanglement purification. , 2013, Physical review letters.

[31]  Fu-Guo Deng,et al.  Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities , 2013, 1310.0197.

[32]  Fu-Guo Deng,et al.  Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity. , 2013, Optics express.

[33]  Wolfgang Dur,et al.  Effective noise channels for encoded quantum systems , 2013, 1306.1738.

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

[35]  Ting Gao,et al.  Preparation of km-photon concatenated Greenberger–Horne–Zeilinger states for observing distinctive quantum effects at macroscopic scales , 2013 .

[36]  B. Kraus,et al.  Improved Quantum Metrology Using Quantum Error Correction , 2013, 1310.3750.

[37]  S. Fei,et al.  Entanglement Detection Using Mutually Unbiased Measurements , 2014, 1407.0314.

[38]  Fu-Guo Deng,et al.  Two-step hyperentanglement purification with the quantum-state-joining method , 2014, 1408.0048.

[39]  Ping Xu,et al.  Experimental realization of a concatenated Greenberger–Horne–Zeilinger state for macroscopic quantum superpositions , 2014 .

[40]  Wolfgang Dür,et al.  Robustness of hashing protocols for entanglement purification , 2014 .

[41]  Yu-Bo Sheng,et al.  Deterministic polarization entanglement purification using time-bin entanglement , 2013, 1311.0470.

[42]  Lan Zhou,et al.  Deterministic entanglement distillation for secure double-server blind quantum computation , 2013, Scientific Reports.

[43]  Guang Ping He,et al.  Security bound of cheat sensitive quantum bit commitment , 2014, Scientific Reports.

[44]  Lan Zhou,et al.  Entanglement concentration for concatenated Greenberger–Horne–Zeilinger state , 2015, Quantum Inf. Process..

[45]  Lan Zhou,et al.  Two-step complete polarization logic Bell-state analysis , 2014, Scientific Reports.

[46]  Fuguo Deng,et al.  Heralded high-efficiency quantum repeater with atomic ensembles assisted by faithful single-photon transmission , 2015, Scientific Reports.

[47]  Jiangfeng Du,et al.  Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions , 2015, Nature Communications.

[48]  Tian-Yin Wang,et al.  Security of quantum digital signatures for classical messages , 2015, Scientific Reports.

[49]  Yu-Bo Sheng,et al.  Entanglement analysis for macroscopic Schrödinger's Cat state , 2015 .

[50]  Run-hua Shi,et al.  Two Quantum Protocols for Oblivious Set-member Decision Problem , 2015, Scientific Reports.

[51]  Yu-Bo Sheng,et al.  Complete logic Bell-state analysis assisted with photonic Faraday rotation , 2015 .

[52]  Xi Chen,et al.  Expected number of quantum channels in quantum networks , 2015, Scientific Reports.

[53]  Lan Zhou,et al.  Efficient entanglement concentration for concatenated Greenberger–Horne–Zeilinger state with the cross-Kerr nonlinearity , 2016, Quantum Inf. Process..

[54]  Gui-Lu Long,et al.  Experimental quantum secure direct communication with single photons , 2015, Light: Science & Applications.

[55]  Lan Zhou,et al.  Feasible logic Bell-state analysis with linear optics , 2015, Scientific Reports.

[56]  Zach DeVito,et al.  Opt , 2017 .