Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

[1]  Generation of macroscopic superposition states with small nonlinearity , 2004, quant-ph/0405041.

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

[3]  B. Yurke,et al.  Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. , 1986, Physical review letters.

[4]  L.-M. Duan,et al.  Engineering superpositions of coherent states in coherent optical pulses through cavity-assisted interaction , 2005 .

[5]  G. J. Milburn,et al.  Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping , 1998, quant-ph/9809037.

[6]  Radim Filip,et al.  Entanglement concentration of continuous-variable quantum states , 2003 .

[7]  O. Hirota,et al.  Entangled coherent states: Teleportation and decoherence , 2001 .

[8]  Konrad Banaszek,et al.  Nonlocality of the Einstein-Podolsky-Rosen state in the Wigner representation , 1998 .

[9]  William H. Press,et al.  Numerical recipes , 1990 .

[10]  Quantum nonlocality of N-qubit W states , 2005, quant-ph/0510013.

[11]  J. Cirac,et al.  Three qubits can be entangled in two inequivalent ways , 2000, quant-ph/0005115.

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

[13]  G. Milburn,et al.  Quantum computation with optical coherent states , 2002, QELS 2002.

[14]  Production of superpositions of coherent states in traveling optical fields with inefficient photon detection , 2004, quant-ph/0410022.

[15]  S. Harris,et al.  Light speed reduction to 17 metres per second in an ultracold atomic gas , 1999, Nature.

[16]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[17]  Kiel T. Williams,et al.  Extreme quantum entanglement in a superposition of macroscopically distinct states. , 1990, Physical review letters.

[18]  M. Kafatos.  Bell's theorem, quantum theory and conceptions of the universe , 1989 .

[19]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[20]  B. S. Ham,et al.  Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime , 2003 .

[21]  Sanders,et al.  Entangled coherent states. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  J. Franson,et al.  Violation of Bell's inequality with photons from independent sources. , 2003, Physical review letters.

[23]  Jinhyoung Lee,et al.  Quantum-information processing for a coherent superposition state via a mixedentangled coherent channel , 2001, quant-ph/0104090.

[24]  Measuring quantum state overlaps of traveling optical fields , 1999, quant-ph/9910029.

[25]  Xiaoguang Wang.  Quantum teleportation of entangled coherent states , 2001 .

[26]  Konrad Banaszek,et al.  TESTING QUANTUM NONLOCALITY IN PHASE SPACE , 1999 .

[27]  Vogel,et al.  Unbalanced homodyning for quantum state measurements. , 1996, Physical review. A, Atomic, molecular, and optical physics.

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

[29]  Nguyen Ba An,et al.  Teleportation of coherent-state superpositions within a network , 2003 .

[30]  L. Knoll,et al.  GENERATION OF ARBITRARY QUANTUM STATES OF TRAVELING FIELDS , 1999 .

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

[32]  M. S. Kim,et al.  Efficient quantum computation using coherent states , 2001, quant-ph/0109077.

[33]  Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime , 2003 .

[34]  R. Brouri,et al.  Non-gaussian statistics from individual pulses of squeezed light , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[35]  Milburn,et al.  Quantum theory of optical feedback via homodyne detection. , 1993, Physical review letters.

[36]  M. Kim,et al.  Quantum nonlocality for a mixed entangled coherent state , 2001, quant-ph/0109121.

[37]  N. An.  Optimal processing of quantum information via W-type entangled coherent states , 2004 .

[38]  Maximal violation of Bell inequalities using continuous-variable measurements , 2002, quant-ph/0211067.

[39]  W. Son,et al.  Quantum nonlocality test for continuous-variable states with dichotomic observables , 2002, quant-ph/0210110.

[40]  Shigeki Takeuchi,et al.  Development of a high-quantum-efficiency single-photon counting system , 1999 .

[41]  T. Ralph,et al.  Transmission of optical coherent-state qubits , 2003, quant-ph/0311093.

[42]  Lossy purification and detection of entangled coherent states , 2002, quant-ph/0203144.

[43]  M. Horne,et al.  Experimental Consequences of Objective Local Theories , 1974 .

[44]  M. S. Kim,et al.  Purification of entangled coherent states , 2002, Quantum Inf. Comput..

[45]  Munro,et al.  Bell's inequality for an entanglement of nonorthogonal states. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[46]  Gerard J. Milburn,et al.  Quantum computation based on linear optics , 2002, SPIE/COS Photonics Asia.

[47]  Hyunseok Jeong,et al.  Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation , 2005, quant-ph/0507095.

[48]  A. P. Lund,et al.  Conditional production of superpositions of coherent states with inefficient photon detection , 2004 .

[49]  Banaszek,et al.  Direct probing of quantum phase space by photon counting. , 1996, Physical review letters.

[50]  Francesco De Martini.  Amplification of Quantum Entanglement , 1998 .

[51]  Adan Cabello.  Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states , 2002 .

[52]  Generating entangled superpositions of macroscopically distinguishable states within a parametric oscillator , 1999, quant-ph/9902082.

[53]  M. Kim,et al.  Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime , 2003, quant-ph/0302059.