scholarly journals Non-Gaussianity of Four-Photon Superpositions of Fock States

2021 ◽  
Vol 3 (3) ◽  
pp. 350-365
Author(s):  
Miguel Citeli de Freitas ◽  
Viktor V. Dodonov
Keyword(s):  
Fourth Order ◽  
Effective Temperature ◽  
Coherent States ◽  
Squeezed States ◽  
Gaussian States ◽  
Fock States ◽  
The Past ◽  
Fidelity Measure ◽  
Non Gaussian ◽  
Thermal States

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

Teleportation improvement by noiseless linear amplification

2019 ◽  
Vol 19 (11&12) ◽  
pp. 935-951
Author(s):  
Hamza Adnane ◽  
Matteo G.A. Paris
Keyword(s):  
Coherent States ◽  
Large Range ◽  
Low Energy ◽  
Entangled State ◽  
Continuous Variables ◽  
Linear Amplification ◽  
Gaussian States ◽  
Linear Amplifier ◽  
Twin Beam ◽  
Non Gaussian

We address de-Gaussification of continuous variables Gaussian states by optimal non-deterministic noiseless linear amplifier (NLA) and analyze in details the properties of the amplified states. In particular, we investigate the entanglement content and the non-Gaussian character for the class of non-Gaussian entangled state obtained by using NL-amplification of two-mode squeezed vacua (twin-beam, TWB). We show that entanglement always increases, whereas improved EPR correlations are observed only when the input TWB has low energy. We then examine a Braunstein-Kimble-like protocol for the teleportation of coherent states, and compare the performances of TWB-based teleprotation with those obtained using NL-amplified resources. We show that teleportation fidelity and security may be improved for a large range of NLA parameters (gain and threshold).

scholarly journals ENTANGLEMENT CRITERION FOR COHERENT SUBTRACTION AND COHERENT ADDITION OF BIPARTITE CONTINUOUS VARIABLE STATES

2013 ◽  
Vol 11 (06) ◽  
pp. 1350060
Author(s):  
LI-ZHEN JIANG ◽  
XIAO-YU CHEN ◽  
TIAN-YU YE ◽  
FANG-YU HONG ◽  
LIANG-NENG WU
Keyword(s):  
Thermal Noise ◽  
Photon Number ◽  
Sufficient Conditions ◽  
Continuous Variable ◽  
Entangled State ◽  
Gaussian States ◽  
Non Gaussian ◽  
Entanglement Criterion ◽  
Entanglement Conditions ◽  
Thermal States

We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

scholarly journals EXPERIMENTAL QUANTIFICATION OF NON-GAUSSIANITY OF PHASE-RANDOMIZED COHERENT STATES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241006 ◽  
Author(s):  
ALESSIA ALLEVI ◽  
STEFANO OLIVARES ◽  
MARIA BONDANI
Keyword(s):  
Experimental Investigation ◽  
Wigner Function ◽  
Coherent States ◽  
The Other ◽  
Fock States ◽  
Two Measures ◽  
Non Gaussian

We present the experimental investigation of the non-Gaussian nature of some mixtures of Fock states by reconstructing their Wigner function and exploiting two recently introduced measures of non-Gaussianity. In particular, we demonstrate the consistency between the different approaches and the monotonicity of the two measures for states belonging to the class of phase-randomized coherent states. Moreover, we prove that the exact behavior of one measure with respect to the other depends on the states under investigation and devise possible criteria to discriminate which measure is more useful for the characterization of the states in realistic applications.

Continuous-variable quantum optical experiments in the time domain using squeezed states and heralded non-Gaussian states

2017 ◽  
Author(s):  
Jun-ichi Yoshikawa ◽  
Yosuke Hashimoto ◽  
Hisashi Ogawa ◽  
Shota Yokoyama ◽  
Yu Shiozawa ◽  
...  
Keyword(s):  
Time Domain ◽  
Continuous Variable ◽  
Squeezed States ◽  
Gaussian States ◽  
Non Gaussian ◽  
The Time Domain ◽  
Quantum Optical

ON THE SEMICLASSICAL LIMIT OF LOOP QUANTUM COSMOLOGY

2012 ◽  
Vol 21 (09) ◽  
pp. 1250076 ◽  
Author(s):  
ALEJANDRO CORICHI ◽  
EDISON MONTOYA
Keyword(s):  
Coherent State ◽  
Quantum Cosmology ◽  
Coherent States ◽  
Semiclassical Limit ◽  
Loop Quantum Cosmology ◽  
Squeezed States ◽  
Gaussian States ◽  
Exactly Solvable ◽  
Spatial Topology ◽  
Frw Model

We consider a k = 0 Friedman–Robertson–Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state solutions for each point on the space of classical states. We propose physical criteria that select from these coherent states, those that display semiclassical behavior, and study their properties in the deep Planck regime. Furthermore, we consider generalized squeezed states and compare them to the Gaussian states. The issue of semiclassicality preservation across the bounce is studied and shown to be generic for all the states considered. Finally, we comment on some implications these results have, depending on the topology of the spatial slice. In particular, we consider the issue of the recovery, within our class of states, of a scaling symmetry present in the classical description of the system when the spatial topology is noncompact.

scholarly journals Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states

2006 ◽  
Vol 73 (4) ◽  
Author(s):  
Akira Kitagawa ◽  
Masahiro Takeoka ◽  
Masahide Sasaki ◽  
Anthony Chefles
Keyword(s):  
Squeezed States ◽  
Gaussian States ◽  
Photon Subtraction ◽  
Non Gaussian

SECOND-ORDER CORRELATION FUNCTION FOR SUCCESSIVE SQUEEZED STATES

1999 ◽  
Vol 13 (29n30) ◽  
pp. 1063-1073 ◽  
Author(s):  
V. A. POPESCU
Keyword(s):  
Correlation Function ◽  
Coherent States ◽  
Second Order ◽  
Statistical Properties ◽  
Squeezed States ◽  
Quantum Statistical ◽  
Thermal States

By successive application of the squeeze operator, we obtain different quantum statistical properties for the squeezed number, the squeezed thermal, the squeezed coherent and the displaced squeezed thermal states. We compare our enhanced squeezing method with other procedures for superposition of two squeezed coherent states.

scholarly journals Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 980
Author(s):  
Miguel Citeli de Freitas ◽  
Vitor Dantas Meireles ◽  
Viktor V. Dodonov
Keyword(s):  
Lower Bounds ◽  
Coherent States ◽  
High Order ◽  
Point Of View ◽  
Squeezed States ◽  
Mean Values ◽  
Fock States

We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson–Schrödinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced.

scholarly journals Non-Gaussianity of Four-Photon Superpositions of Fock States

2021 ◽  
Author(s):  
Viktor V. Dodonov ◽  
Miguel de Freitas Citeli
Keyword(s):  
Coherent States ◽  
Squeezed States ◽  
Fock States

We compare several different measures of non-Gaussianity for two families of four-photon superpositions of the Fock states: even vacuum squeezed states and orthogonal-even coherent states.

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