Complete hyperentangled-Bell-state analysis for photonic qubits assisted by a three-level Λ-type system

Hyperentangled Bell-state analysis (HBSA) is an essential method in high-capacity quantum communication and quantum information processing. Here by replacing the two-qubit controlled-phase gate with the two-qubit SWAP gate, we propose a scheme to distinguish the 16 hyperentangled Bell states completely in both the polarization and the spatial-mode degrees of freedom (DOFs) of two-photon systems. The proposed scheme reduces the use of two-qubit interaction which is fragile and cumbersome, and only one auxiliary particle is required. Meanwhile, it reduces the requirement for initializing the auxiliary particle which works as a temporary quantum memory, and does not have to be actively controlled or measured. Moreover, the state of the auxiliary particle remains unchanged after the HBSA operation, and within the coherence time, the auxiliary particle can be repeatedly used in the next HBSA operation. Therefore, the engineering complexity of our HBSA operation is greatly simplified. Finally, we discuss the feasibility of our scheme with current technologies.

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

[2]  Paul G. Kwiat,et al.  Hyperentangled Bell-state analysis , 2007 .

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

[4]  N. Gisin,et al.  Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication , 1999 .

[5]  Shih,et al.  New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. , 1988, Physical review letters.

[6]  Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement , 2011, 1109.1584.

[7]  A Gilchrist,et al.  Measuring entangled qutrits and their use for quantum bit commitment. , 2004, Physical review letters.

[8]  N Gisin,et al.  Quantum teleportation with a three-Bell-state analyzer. , 2005, Physical review letters.

[9]  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 .

[10]  John Calsamiglia.  Generalized measurements by linear elements , 2002 .

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

[12]  Christian Nölleke,et al.  Ground-state cooling of a single atom at the center of an optical cavity. , 2012, Physical review letters.

[13]  Yan Xia,et al.  Quantum gate operations using atomic qubits through cavity input-output process , 2009 .

[14]  Tzonelih Hwang,et al.  Comment on 'Quantum secret sharing between multiparty and multiparty without entanglement' , 2006 .

[15]  Yasunobu Nakamura,et al.  Deterministic photon-photon √ SWAP gate using a system , 2010 .

[16]  Atsushi Yabushita,et al.  Spectroscopy by frequency-entangled photon pairs , 2004 .

[17]  Anders Karlsson,et al.  Security of quantum key distribution using d-level systems. , 2001, Physical review letters.

[18]  D. Bruß,et al.  Optimal eavesdropping in cryptography with three-dimensional quantum states. , 2001, Physical review letters.

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

[20]  F De Martini,et al.  All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement. , 2005, Physical review letters.

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

[22]  H. Kimble,et al.  Scalable photonic quantum computation through cavity-assisted interactions. , 2004, Physical review letters.

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

[24]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[25]  J. Rarity,et al.  Experimental violation of Bell's inequality based on phase and momentum. , 1990, Physical review letters.

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

[27]  Xuedong Hu,et al.  Efficient purification protocols using iSWAP gates in solid-state qubits , 2008, 0807.4788.

[28]  Weinfurter,et al.  Dense coding in experimental quantum communication. , 1996, Physical review letters.

[29]  Cristian Bonato,et al.  CNOT and Bell-state analysis in the weak-coupling cavity QED regime. , 2010, Physical review letters.

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

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

[32]  Dirk Englund,et al.  Controlled Phase Shifts with a Single Quantum Dot , 2008, Science.

[33]  Jian-Wei Pan,et al.  Quantum teleportation of multiple degrees of freedom of a single photon , 2015, Nature.

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

[35]  Shih,et al.  Postselection-free energy-time entanglement. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[36]  Law,et al.  Modification of a vacuum Rabi splitting via a frequency-modulated cavity mode. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[37]  G. Vallone,et al.  Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement , 2006, quant-ph/0609080.

[38]  A. Imamoğlu,et al.  Single photon absorption by a single quantum emitter. , 2007, Physical review letters.

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

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

[41]  Jian-Wei Pan,et al.  Efficient multiparty quantum-secret-sharing schemes , 2004, quant-ph/0405179.

[42]  C. Hamley,et al.  Cavity QED with optically transported atoms , 2003, quant-ph/0309052.

[43]  Ou,et al.  Violation of Bell's inequality and classical probability in a two-photon correlation experiment. , 1988, Physical review letters.

[44]  K. Koshino,et al.  Deterministic photon-photon (SWAP)^{1/2} gate using a lambda system , 2009, 0909.4762.

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

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

[47]  Efficient and high-fidelity generation of atomic cluster states with cavity QED and linear optics , 2007, quant-ph/0703116.

[48]  F. Nori,et al.  Superconducting Circuits and Quantum Information , 2005, quant-ph/0601121.

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

[50]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

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

[52]  Franco Nori,et al.  Probing tiny motions of nanomechanical resonators: classical or quantum mechanical? , 2006, Physical review letters.

[53]  Evelyn L. Hu,et al.  Ultrafast all-optical switching by single photons , 2011, Nature Photonics.

[54]  Christian Kurtsiefer,et al.  Complete deterministic linear optics Bell state analysis. , 2006, Physical review letters.

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

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

[57]  M. Lukin,et al.  All-Optical Switch and Transistor Gated by One Stored Photon , 2013, Science.

[58]  Franson,et al.  Bell inequality for position and time. , 1989, Physical review letters.

[59]  A. Zeilinger,et al.  Communications: Quantum teleportation across the Danube , 2004, Nature.