Practical entanglement concentration of nonlocal polarization-spatial hyperentangled states with linear optics

We present some different hyperentanglement concentration protocols (hyper-ECPs) for nonlocal N-photon systems in partially polarization-spatial hyperentangled states with known parameters, resorting to linear optical elements only, including those for hyperentangled Greenberger–Horne–Zeilinger-class states and the ones for hyperentangled cluster-class states. Our hyper-ECPs have some interesting features. First, they require only one copy of nonlocal N-photon systems and do not resort to ancillary photons. Second, they work with linear optical elements, neither Bell-state measurement nor two-qubit entangling gates. Third, they have the maximal success probability with only a round of entanglement concentration, not repeating the concentration process some times. Fourth, they resort to some polarizing beam splitters and wave plates, not unbalanced beam splitters, which make them more convenient in experiment.

[1]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[2]  Yimin Liu,et al.  Four-party deterministic operation sharing with six-qubit cluster state , 2014, Quantum Inf. Process..

[3]  G. Long,et al.  General scheme for superdense coding between multiparties , 2001, quant-ph/0110112.

[4]  Shohini Ghose,et al.  Hyperentanglement concentration for time-bin and polarization hyperentangled photons , 2015, 1502.02891.

[5]  Ping Zhou,et al.  Linear-Optics-Based Bidirectional Controlled Remote State Preparation via Five-Photon Cluster-Type States for Quantum Communication Network , 2016 .

[6]  Yan Xia,et al.  Efficient entanglement concentration for partially entangled cluster states with weak cross-Kerr nonlinearity , 2015, Quantum Inf. Process..

[7]  Ahmed Farouk,et al.  A scheme for secure quantum communication network with authentication using GHZ-like states and cluster states controlled teleportation , 2015, Quantum Information Processing.

[8]  S. Bose,et al.  PURIFICATION VIA ENTANGLEMENT SWAPPING AND CONSERVED ENTANGLEMENT , 1998, quant-ph/9812013.

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

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

[11]  Fuguo Deng,et al.  Heralded entanglement concentration for photon systems with linear-optical elements , 2015 .

[12]  Wei Zhang,et al.  Quantum Secure Direct Communication with Quantum Memory. , 2016, Physical review letters.

[13]  Fuguo Deng,et al.  Quantum secure direct communication with high-dimension quantum superdense coding , 2005 .

[14]  T. Wei,et al.  Beating the channel capacity limit for linear photonic superdense coding , 2008 .

[15]  Shohini Ghose,et al.  Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity , 2016 .

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

[17]  Fu-Guo Deng,et al.  Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities. , 2012, Optics express.

[18]  Lan Zhou,et al.  Efficient N-particle W state concentration with different parity check gates , 2012, 1204.1492.

[19]  G. Vallone,et al.  Experimental entanglement and nonlocality of a two-photon six-qubit cluster state. , 2009, Physical review letters.

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

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

[22]  Tie-Jun Wang,et al.  Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities , 2012 .

[23]  M. Koashi,et al.  Concentration and purification scheme for two partially entangled photon pairs , 2001, quant-ph/0101042.

[24]  Yu-Bo Sheng,et al.  Arbitrary Four-Photon Cluster State Concentration with Cross-Kerr Nonlinearity , 2015 .

[25]  Guang-Can Guo,et al.  Multiuser-to-multiuser entanglement distribution based on 1550 nm polarization-entangled photons , 2015 .

[26]  Qian Liu,et al.  Efficient hyperentanglement purification for two-photon six-qubit quantum systems , 2016 .

[27]  Fu-Guo Deng,et al.  Hyper-parallel photonic quantum computation with coupled quantum dots , 2013, Scientific Reports.

[28]  Girish S. Agarwal,et al.  Entanglement of polarization and orbital angular momentum , 2015 .

[29]  Wenjie Liu,et al.  Cryptanalysis of Controlled Quantum Secure Direct Communication and Authentication Protocol Based on Five-Particle Cluster State and Quantum One-Time Pad , 2016 .

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

[31]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[32]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[33]  Ying-Dan Wang,et al.  Entanglement concentration with strong projective measurement in an optomechanical system , 2015 .

[34]  Tie-Jun Wang,et al.  Concentration and distribution of entanglement based on valley qubits system in graphene , 2015 .

[35]  Nicolas Gisin,et al.  Quantum repeaters based on atomic ensembles and linear optics , 2009, 0906.2699.

[36]  Yan Xia,et al.  Efficient hyperentanglement concentration for N-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity , 2016, Quantum Inf. Process..

[37]  Xi-Han Li,et al.  Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity. , 2015, Optics express.

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

[39]  Fuguo Deng.  Optimal nonlocal multipartite entanglement concentration based on projection measurements , 2011, 1112.1355.

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

[41]  Yu-Bo Sheng,et al.  Purification of Logic-Qubit Entanglement , 2015, Scientific Reports.

[42]  Fu-Guo Deng,et al.  Practical hyperentanglement concentration for two-photon four-qubit systems with linear optics , 2013, 1306.0050.

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

[44]  Harald Weinfurter,et al.  Embedded Bell-state analysis , 1998 .

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

[46]  Jian-Wei Pan,et al.  Practical scheme for entanglement concentration , 2001, quant-ph/0104039.

[47]  Fu-Guo Deng,et al.  Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities , 2013, 1309.0168.

[48]  Qian Liu,et al.  Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators , 2015, 1507.06108.

[49]  Qing Ai,et al.  Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities. , 2016, Optics express.

[50]  S. Walborn,et al.  Hyperentanglement-assisted Bell-state analysis , 2003, quant-ph/0307212.

[51]  Ru Zhang,et al.  One-step hyperentanglement purification and hyperdistillation with linear optics. , 2015, Optics express.

[52]  Marco Barbieri,et al.  Polarization-momentum hyperentangled states : Realization and characterization , 2005 .

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

[54]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[55]  Nicolas Godbout,et al.  Cluster-state quantum computing in optical fibers , 2007 .

[56]  Gui-Lu Long,et al.  Quantum secure direct communication , 2011 .

[57]  Gui-Lu Long,et al.  Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities , 2016 .

[58]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

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

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

[61]  Chuan Wang,et al.  Nonlocal hyperconcentration on entangled photons using photonic module system , 2016 .

[62]  G. Guo,et al.  Optimal entanglement purification via entanglement swapping , 2000, quant-ph/0005125.

[63]  Tao Li,et al.  High-efficiency atomic entanglement concentration for quantum communication network assisted by cavity QED , 2015, Quantum Inf. Process..

[64]  Ru Zhang,et al.  Cluster state entanglement generation and concentration on nitrogen-vacancy centers in decoherence-free subspace , 2015 .

[65]  Charles H. Bennett,et al.  Quantum cryptography without Bell's theorem. , 1992, Physical review letters.

[66]  Tie-Jun Wang,et al.  Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities , 2012 .

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

[68]  Fuguo Deng,et al.  Reply to ``Comment on `Secure direct communication with a quantum one-time-pad' '' , 2004, quant-ph/0405177.

[69]  Shohini Ghose,et al.  Hyperconcentration for multipartite entanglement via linear optics , 2014, 1601.03755.

[70]  Fang-Fang Du,et al.  Refined hyperentanglement purification of two-photon systems for high-capacity quantum communication with cavity-assisted interaction , 2016 .

[71]  Gui-Lu Long,et al.  Refined entanglement concentration for electron-spin entangled cluster states with quantum-dot spins in optical microcavities , 2017, Quantum Inf. Process..

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

[73]  Yan Xia,et al.  Efficient entanglement concentration for arbitrary less-hyperentanglement multi-photon W states with linear optics , 2014, Quantum Information Processing.

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

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

[76]  Cong Cao,et al.  Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements , 2016 .

[77]  Nathan K Langford,et al.  Generation of hyperentangled photon pairs. , 2005, Physical review letters.

[78]  Fu-Guo Deng,et al.  Quantum hyperentanglement and its applications in quantum information processing. , 2016, Science bulletin.

[79]  Bao-Cang Ren,et al.  General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. , 2014, Optics express.

[80]  Bao-Cang Ren,et al.  Highly efficient hyperentanglement concentration with two steps assisted by quantum swap gates , 2015, Scientific Reports.

[81]  Cong Cao,et al.  Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime. , 2013, Optics express.

[82]  Marek Zukowski,et al.  All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement. , 2005, Physical review letters.

[83]  G. Vallone,et al.  Hyperentanglement of two photons in three degrees of freedom , 2008, 0810.4461.

[84]  Yu-Bo Sheng,et al.  Complete hyperentangled-Bell-state analysis for quantum communication , 2010, 1103.0230.

[85]  Paul G. Kwiat,et al.  Hyper-entangled states , 1997 .

[86]  Chitra Shukla,et al.  Maximal entanglement concentration for a set of $$(n+1)$$(n+1)-qubit states , 2015, Quantum Inf. Process..

[87]  Yan Yu,et al.  Asymmetric Bidirectional Controlled Teleportation via Seven-qubit Cluster State , 2016 .

[88]  Chuan Wang,et al.  Efficient multipartite entanglement concentration protocol for nitrogen-vacancy center and microresonator coupled systems , 2015, Quantum Inf. Process..

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

[90]  Fu-Guo Deng,et al.  Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime , 2014, 1411.0274.

[91]  Chitra Shukla,et al.  Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states , 2014, Quantum Inf. Process..

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

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

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