Entanglement generation with deformed Barut-Girardello coherent states as input states in an unitary beam splitter

Using linear entropy as a measure of entanglement, we investigate the entanglement generated via a beam splitter using deformed Barut-Girardello coherent states. We show that the degree of entanglement depends strongly on the q-deformation parameter and amplitude Z of the states. We compute the Mandel Q parameter to examine the quantum statistical properties of these coherent states and make a comparison with the Glauber coherent states. It is shown that these states are useful in describing the states of real and ideal lasers by a proper choice of their characterizing parameters, using an alteration of the Holstein-Primakoff realization.

[1]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[2]  Hall,et al.  Generation of squeezed states by parametric down conversion. , 1986, Physical review letters.

[3]  M. Teich,et al.  Observation of sub-Poisson Franck-Hertz light at 253. 7 nm , 1984 .

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

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

[6]  E. Curado,et al.  Coherent states for a degenerate system: The hydrogen atom , 2006 .

[7]  L. Kuang,et al.  The suq(1,1) q-coherent states and their nonclassical properties , 1993 .

[8]  Pérès.  Separability Criterion for Density Matrices. , 1996, Physical review letters.

[9]  S. Vasan,et al.  On completeness of Barut–Girardello coherent states of suq(1, 1) algebra , 2004 .

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

[11]  R. Jozsa,et al.  Quantum Computation and Shor's Factoring Algorithm , 1996 .

[12]  Mario Dagenais,et al.  Photon Antibunching in Resonance Fluorescence , 1977 .

[13]  C. Nelson,et al.  The q-analogue quantized radiation field and its uncertainty relations , 1992 .

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

[15]  E. Bagan,et al.  Phase estimation for thermal Gaussian states , 2008, 0811.3408.

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

[17]  K. Schmüdgen,et al.  Quantum Groups and Their Representations , 1998 .

[18]  P. L. Knight,et al.  Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement , 2002 .

[19]  G. Tóth,et al.  Entanglement detection based on interference and particle counting (6 pages) , 2003, quant-ph/0306086.

[20]  Collett,et al.  Nonlocality of a single photon. , 1991, Physical review letters.

[21]  Jan Peřina,et al.  Quantum optics and fundamentals of physics , 1994 .

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

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

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

[25]  B. Jurčo.  On coherent states for the simplest quantum groups , 1991 .

[26]  G. Milburn,et al.  Universal state inversion and concurrence in arbitrary dimensions , 2001, quant-ph/0102040.

[27]  S. Chaturvedi,et al.  Unified approach to the analogues of single-photon and multiphoton coherent states for generalized bosonic oscillators , 1994 .

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

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

[30]  Belgium,et al.  Maximal entanglement versus entropy for mixed quantum states , 2002, quant-ph/0208138.

[31]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

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

[33]  Construction of coherent states for physical algebraic systems (7 pages) , 2004, math-ph/0408030.

[34]  Sean D. Huver,et al.  Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing , 2008, 0805.0296.

[35]  A. Perelomov.  The Erwin Schrr Odinger International Institute for Mathematical Physics on the Completeness of Some Subsystems of Q{deformed Coherent States on the Completeness of Some Subsystems of Q-deformed Coherent States , 2022 .

[36]  Ekert,et al.  "Event-ready-detectors" Bell experiment via entanglement swapping. , 1993, Physical review letters.

[37]  Jieci Wang,et al.  Entanglement of coupled massive scalar field in background of dilaton black hole , 2009, 0905.3226.

[38]  Hong,et al.  Higher-order squeezing of a quantum field. , 1985, Physical review letters.

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

[40]  K-component q-deformed charge coherent states and their nonclassical properties , 2005, quant-ph/0503076.

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

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

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

[44]  Chaturvedi,et al.  Generalized commutation relations for a single-mode oscillator. , 1991, Physical review. A, Atomic, molecular, and optical physics.

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

[46]  C. Gerry,et al.  Beam splitting and entanglement: Generalized coherent states, group contraction, and the classical limit , 2005 .

[47]  L. Mandel,et al.  Observation of Sub-Poissonian Photon Statistics , 1983 .

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

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

[50]  A. M. Scarfone,et al.  An interacting ensemble of particles in the context of quantum algebra , 2009 .

[51]  Generation of NPT Entanglement from Nonclassical Photon Statistics , 2006, quant-ph/0603255.

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

[53]  R. Gilmore,et al.  Coherent states: Theory and some Applications , 1990 .

[54]  G. Guo,et al.  Efficient scheme for two-atom entanglement and quantum information processing in cavity QED , 2000, Physical review letters.

[55]  V. Vedral,et al.  Mixedness and teleportation , 2000 .

[56]  A. Uhlmann.  Fidelity and Concurrence of conjugated states , 1999, quant-ph/9909060.

[57]  E. Schrödinger.  Der stetige Übergang von der Mikro- zur Makromechanik , 1926, Naturwissenschaften.

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

[59]  I. Burban.  Arik–Coon oscillator with q > 1 in the framework of unified (q; α, β, γ; ν)-deformation , 2010 .