Entanglement versus noncommutativity in teleportation

Ghosh, Sibasish; Kar, Guruprasad; Roy, Anirban; Sen, Ujjwal

doi:10.1103/physreva.65.032309

Cited by 17 publications

(27 citation statements)

References 13 publications

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“…The Schrödinger group has been defined in [39][40][41] as the largest group of space-time transformations which leaves the Schrödinger equation for a free particle invariant. Schrödinger invariance has been considered in a wide variety of situations, including celestial mechanics [8], non-relativistic field theory [42,43], non-relativistic quantum mechanics [44], and hydrodynamics [45][46][47][48][49]. Mathematical aspects of the Schrödinger symmetry have been analyzed, for instance, in [50].…”

Section: Schrödinger Isometry Group and The Siklos Spacetimesmentioning

confidence: 99%

Deeper discussion of Schrödinger invariant and logarithmic sectors of higher-curvature gravity

Ayón–Beato

Giribet

2011

Phys. Rev. D

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The aim of this paper is to explore D-dimensional theories of pure gravity whose space of solutions contains certain class of AdS-waves, including in particular Schrödinger invariant spacetimes. This amounts to consider higher order theories, and the natural case to start with is to analyze generic square-curvature corrections to Einstein-Hilbert action. In this case, the Schrödinger invariant sector in the space of solutions arises for a special relation between the coupling constants appearing in the action. On the other hand, besides the Schrödinger invariant configurations, logarithmic branches similar to those of the so-called Log-gravity are also shown to emerge for another special choice of the coupling constants. Interestingly enough, these Log solutions can be interpreted as the superposition of the massless mode of General Relativity and two scalar modes that saturate the Breitenlohner-Freedman bound (BF) of the AdS space on which they propagate. These solutions are higher-dimensional analogues of those appearing in three-dimensional massive gravities with relaxed AdS3 asymptotic, which are candidates to be gravity duals for logarithmic CFTs. Other sectors of the space of solutions of higher-curvature theories correspond to oscillatory configurations, which happen to be below the BF bound. Also, there is a fully degenerated sector, for which any wave profile is admitted. We comment on the relation between this degeneracy and the nonrenormalizability of the dynamical exponent of the Schrödinger spaces. Our analysis also includes more general gravitational actions with non-polynomial corrections consisting of arbitrary functions of the square-curvature invariants. By establishing a correspondence with the quadratic gravity model, the same sectors of solutions are shown to exist for this more general family of theories. We finally consider the parity-violating Chern-Simons modified gravity in four dimensions, for which we derive both the Schrödinger invariant as well as the logarithmic sectors.This paper is dedicated to the memory of Laurent Houart.

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Section: Schrödinger Isometry Group and The Siklos Spacetimesmentioning

confidence: 99%

Deeper discussion of Schrödinger invariant and logarithmic sectors of higher-curvature gravity

Ayón–Beato

Giribet

2011

Phys. Rev. D

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“…The exact solution may be found only for particular cases. The qualitative nature of solutions of such systems may be described in terms of the dynamics of various moments [32,33,34,35]. In particular, the moments satisfy a set of coupled first-order differential equations with time as the independent variable.…”

Section: Dynamics Of Momentsmentioning

confidence: 99%

“…However, in general, this is not a close system of differential equations and involve spatial integrals involving fields. An exact time-development of some of the moments may be described analytically for systems with dynamical conformal symmetry [32,33]. Consequently, important information regarding the time-development of the field for different initial conditions may be inferred.…”

Section: Dynamics Of Momentsmentioning

confidence: 99%

Symmetries and exact solutions of a class of nonlocal nonlinear Schrödinger equations with self-induced parity-time-symmetric potential

Sinha

Ghosh

2015

Phys. Rev. E

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A class of non-local non-linear Schrödinger equations(NLSE) is considered in an external potential with space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable non-local NLSE with self-induced potential that is PT symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or non-autonomous non-local NLSE by using similarity transformation and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the non-local NLSE without the external potential and a d + 1 dimensional generalization of it, admits all the symmetries of the d + 1 dimensional Schrödinger group. The conserved Noether charges associated with the time-translation, dilatation and special conformal transformation are shown to be real-valued in spite of being non-hermitian. Finally, dynamics of different moments are studied with an exact description of the time-evolution of the "pseudo-width" of the wave-packet for the special case when the system admits a O(2, 1) conformal symmetry.

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“…In this paper we shall be concerned with the Schrödinger symmetry that is defined as the dynamical symmetry leaving invariant the free Schrödinger equation, see [1], [2] and [3]. The Schrödinger invariance has been relevant in a wide variety of situations as celestial mechanics [4], nonrelativistic field theory [5]- [6], non-relativistic quantum mechanics [7], hydrodynamics [8,9,10,11], in the context of the AdS/CFT correspondence [12] as well as in statistical physics [13].…”

Section: Introductionmentioning

confidence: 99%

Conformal symmetry of an extended Schrödinger equation and its relativistic origin

Hassaïne

2007

J. Phys. A: Math. Theor.

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In this paper two things are done. We first prove that an arbitrary power p of the Schrödinger Lagrangian in arbitrary dimension always enjoys the non-relativistic conformal symmetry. The implementation of this symmetry on the dynamical field involves a phase term as well as a conformal factor that depends on the dimension and on the exponent. This non-relativistic conformal symmetry is shown to have its origin on the conformal isometry of the power p of the Klein-Gordon Lagrangian in one higher dimension which is related to the phase of the complex scalar field.

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Entanglement versus noncommutativity in teleportation

Cited by 17 publications

References 13 publications

Deeper discussion of Schrödinger invariant and logarithmic sectors of higher-curvature gravity

Deeper discussion of Schrödinger invariant and logarithmic sectors of higher-curvature gravity

Symmetries and exact solutions of a class of nonlocal nonlinear Schrödinger equations with self-induced parity-time-symmetric potential

Conformal symmetry of an extended Schrödinger equation and its relativistic origin

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