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arXiv:1506.08901 · International Journal of Modern Physics B

Nonclassicality versus entanglement in a noncommutative space

Sanjib Dey, Andreas Fring, Véronique Hussin

Published Oct 6, 2016• 34 citations
arXivHTMLPDF

Abstract

Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.

DOI
10.1142/s0217979216502489

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Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.
We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite having classical-like behavior, coherent states in noncommutative space produce a small amount of entanglement and therefore they possess slight nonclassicality as well, which is not true for the coherent states of an ordinary harmonic oscillator.
We study several classical-like properties of qqq-deformed nonlinear coherent states as well as nonclassical behaviors of qqq-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in qqq-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the qqq-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.
Abstract In this paper, we introduce some distinct classes of entangled cat states associated to generalized displaced Fock states. For this purpose, we use the formalism of nonlinear coherent states corresponding to nonlinear oscillator algebra which yields various kinds of f-deformed entangled states. We also take a particular class of Gilmore-Perelomov-type of SU(1, 1) and a class of SU(2) coherent states. We then obtain the amount of entanglement between subsystems of the quantum states of interest by applying the measure of concurrence. Furthermore, examining some of the most important criteria, such as Mandels Q parameter, quadrature squeezing and Vogels characteristic function, we study the nonclassicality of the introduced quantum states. The numerical results show remarkable values of entanglement, sub-Poissonian statistics of the field, and squeezing indicating that the introduced states can be regarded as possible candidates for nonclassical entangled states. Afterwards, we see that the Vogel function for quantum states of interests goes beyond the value of characteristic function of the ground state, which shows the nonclassicality of the introduced states.
Nonclassicality is a useful quantum resource in quantum information and has important applications in various quantum tasks such as quantum computing, quantum communication. The robustness of nonclassicality is used to quantify the nonclassicality. The nonclassicality of number states, squeezed states and cat states has been known. We consider the nonclassicality of the squeezed number states. Several different upper and lower bounds for the nonclassicality of squeezed single photon state are obtained through analytical calculation, modeling analysis and numerical calculation. By comparing all these bounds, we find that the nonclassicality of squeezed single photon state can be well determined.
Abstract Superposition of two coherent states, the Schrodinger’s cat state, can exhibit different nonclassical properties having foundational applications in quantum information processing. We consider the ‘superposition of Schrodinger’s cat state with the vacuum state (SCVS)’ of the optical field. We discuss different witness of nonclassicality properties such as lower- and higher-order squeezing (viz., squeezing, Hong & Mandel’s fourth-order squeezing, amplitude-squared squeezing) and sub-Poissonian photon statistics. Further, we discuss the negativity of the Wigner function of SCVS indicating the nonclassicality of the state under investigation. We find that the vacuum state contribution in SCVS exhibits different nonclassicalities under some conditions stronger where the nonclassicalities exhibited by the state without vacuum state contribution are weaker.
Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the "classical-nonclassical polarity," represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features.