Bipartite entanglement of nonlinear quantum systems in the context of the q-Heisenberg Weyl algebra

In this paper, we study in detail the degree of entanglement of bipartite system states in the context of q-Heisenberg-Wely algebra. We examine the entanglement properties for two systems of arbitrary deformation parameters q1 and q2, defined in entanglement of entangled deformed bosonic coherent states of each of the deformation parameters. For a particular choice of the parameters that specify the coherent states, we give conditions under which bipartite entangled coherent states become maximally entangled. We generalize this formalism to the case of bipartite mixed states using a simplified expression of concurrence in Wootters’ measure of the bipartite entanglement.

[1]  Xiaoguang Wang.  Bipartite entangled non-orthogonal states , 2001, quant-ph/0102011.

[2]  Syed Twareque Ali,et al.  Coherent States, Wavelets, and Their Generalizations , 2013 .

[3]  T. Noh.  Counterfactual quantum cryptography. , 2008, Physical review letters.

[4]  J. Eisert,et al.  A comparison of entanglement measures , 1998, quant-ph/9807034.

[5]  A. I. Solomon,et al.  Maximal entanglement of nonorthogonal states: classification , 2001, quant-ph/0105099.

[6]  R. Glauber.  The Quantum Theory of Optical Coherence , 1963 .

[7]  Zheng-Fu Han,et al.  Security of counterfactual quantum cryptography , 2010, 1007.3066.

[8]  G. Bagci,et al.  A note on the definition of deformed exponential and logarithm functions , 2009 .

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

[10]  L. C. Biedenharn,et al.  The quantum group SUq(2) and a q-analogue of the boson operators , 1989 .

[11]  Yong-Sheng Zhang,et al.  Experimental measurement of lower and upper bounds of concurrence for mixed quantum states , 2008, 0808.0776.

[12]  A. J. Macfarlane,et al.  On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q , 1989 .

[13]  H. Eleuch,et al.  Interaction of a quantum well with squeezed light: Quantum-statistical properties , 2010, 1109.4368.

[14]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[15]  M. A. Marchiolli.  On the q-deformed coherent states of a generalized f-oscillator , 2005 .

[16]  P. González-Díaz,et al.  Coherent states in the quantum multiverse , 2009, 0909.3063.

[17]  A. Miranowicz,et al.  Ordering two-qubit states with concurrence and negativity , 2004, quant-ph/0404053.

[18]  Barry C. Sanders,et al.  Entangled coherent states for systems with SU(2) and SU(1,1) symmetries , 2000 .

[19]  William K. Wootters,et al.  Entanglement of formation and concurrence , 2001, Quantum Inf. Comput..

[20]  A. Perelomov.  Coherent states for arbitrary Lie group , 1972 .

[21]  Entanglement via Barut–Girardello coherent state for suq(1,1) quantum algebra: bipartite composite system , 2003, math/0301036.

[22]  H. Eleuch.  Autocorrelation function of microcavity-emitting field in the linear regime , 2008 .

[23]  Tzu-Chieh Wei,et al.  Remote preparation of single-photon "hybrid" entangled and vector-polarization States. , 2010, Physical review letters.

[24]  E. Sudarshan,et al.  f-oscillators and nonlinear coherent states , 1996, quant-ph/9612006.

[25]  R. Schott,et al.  Evolution equations and Lévy processes on quantum groups , 1998 .

[26]  C. Gerry,et al.  Path Integrals and Coherent States of Su(2) and Su(1, 1) , 1992 .

[27]  J. Morton,et al.  Quantum metrology with molecular ensembles , 2010 .

[28]  K. Berrada,et al.  Generalized Heisenberg algebra coherent states for power-law potentials , 2010, 1004.4384.

[29]  Yassine Hassouni,et al.  Entanglement generation with deformed Barut-Girardello coherent states as input states in an unitary beam splitter , 2011, Quantum Inf. Process..

[30]  Dong-Ling Deng,et al.  Bounds of concurrence and their relation with fidelity and frontier states , 2008, 0808.2077.

[31]  S. Solimeno,et al.  PHYSICAL NONLINEAR ASPECTS OF CLASSICAL AND QUANTUM q-OSCILLATORS , 1993 .

[32]  A. Pati,et al.  Perfect teleportation and superdense coding with W states , 2006, quant-ph/0610001.

[33]  Tomoyuki Morimae,et al.  Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation , 2010, 1003.0293.

[34]  Vladimir D. Tonchev,et al.  Entanglement-assisted quantum low-density parity-check codes , 2010, ArXiv.

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

[36]  A. Perelomov.  Generalized Coherent States and Their Applications , 1986 .

[37]  Si-cong,et al.  q-deformed binomial state. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[38]  Mark Hillery,et al.  Entanglement conditions for two-mode states. , 2006, Physical review letters.

[39]  J. Gazeau.  Coherent states in quantum physics: an overview , 2009, Journal of Physics: Conference Series.

[40]  Special deformed exponential functions leading to more consistent Klauder's coherent states , 2002, math-ph/0206016.

[41]  Martin B. Plenio,et al.  An introduction to entanglement measures , 2005, Quantum Inf. Comput..

[42]  Yassine Hassouni,et al.  Concurrence in the framework of coherent states , 2010, Quantum Inf. Process..

[43]  O. Civitarese,et al.  Correspondence between theq-deformed harmonic oscillator and finite range potentials , 2003 .

[44]  M. Nielsen.  Conditions for a Class of Entanglement Transformations , 1998, quant-ph/9811053.

[45]  Howard E. Brandt,et al.  Quantum computation and information : AMS Special Session Quantum Computation and Information, January 19-21, 2000, Washington, D.C. , 2002 .

[46]  N. Reshetikhin,et al.  Quantum Groups , 1993, hep-th/9311069.

[47]  A. Solomon.  GROUP THEORY OF SUPERFLUIDITY. , 1971 .

[48]  Solomon,et al.  Nonideal lasers, nonclassical light, and deformed photon states. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[49]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[50]  K. Berrada,et al.  Maximal entanglement of bipartite spin states in the context of quantum algebra , 2011 .

[51]  S. Popescu,et al.  Thermodynamics and the measure of entanglement , 1996, quant-ph/9610044.

[52]  V. Dodonov.  REVIEW ARTICLE: `Nonclassical' states in quantum optics: a `squeezed' review of the first 75 years , 2002 .

[53]  R. Glauber.  Coherent and incoherent states of the radiation field , 1963 .

[54]  H. Eleuch,et al.  Nonlinear dissipation and the quantum noise of light in semiconductor microcavities , 2004 .

[55]  Y. Hassouni,et al.  Entanglement generation from deformed spin coherent states using a beam splitter , 2009 .

[56]  K. Kokkotas,et al.  WKB equivalent potentials for the q-deformed harmonic oscillator , 1991 .

[57]  C. Gerry,et al.  Maximal violations of a Bell inequality by entangled spin-coherent states , 2009 .

[58]  Sauro Succi,et al.  Galilean-invariant lattice-Boltzmann models with H theorem. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Jr.,et al.  Continuous-variable teleportation of a negative Wigner function , 2010, 1012.5616.

[60]  M. T. Cunha,et al.  Continuous quantum error correction through local operations , 2010, 1009.4744.

[61]  H. Eleuch.  Photon statistics of light in semiconductor microcavities , 2008 .

[62]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.