A monochromatic double-mode coherent light endowed with orthogonally polarized photons propagating collinearly is studied in Degenerate Parametric Amplification. Generation of Hidden Optical- Polarized States is shown by non-zero values of Index of Hidden Optical-Polarization. Squeezing in HOPS is demonstrated by recognizing a Squeezing function. The Non-Classical feature of HOPS is observed by 'degree of Hidden Optical-Polarization' which attains non-classical value 'greater than unity'. The dynamical nature of Generation, Squeezing and Non-Classicality are numerically presented.
We observe the polarization squeezing in the mixture of a two mode squeezed vacuum and a simple coherent light through a linear polarization beam splitter. Squeezed vacuum not being squeezed in polarization, generates polarization squeezed light when superposed with coherent light. All the three Stokes parameters of the light produced on the output port of polarization beam splitter are found to be squeezed and squeezing factor also depends upon the parameters of coherent light.
Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits w…
This paper aims to stress the role of the Cahill-Glauber quasi-probability densities in defining, detecting, and quantifying the non-classicality of field states in quantum optics. The distance between a given pure state and the set of all pure classical states is called here a geometric degree of non-classicality. As such, we investigate non-classicality of a pure single-mode state of the radiation field by using the coherent states as a reference set of pure classical states. It turns out that any such distance is expressed in terms of the maximal value of the Husimi $Q$ function. As an insi…
The well known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results…
The dynamic feature of monochromatic bi-modal chaotic optical field, enriched with orthogonally-polarized basis-modes propagating collinearly and undergoing Degenerate Parametric Amplification, is investigated to demonstrate Squeezing in Hidden Optical-Polarization states. The Variance (Noise) of Hidden Optical-Polarization Parameters showing squeezing therein is numerically studied by identifying a Squeezing - Function. This squeezing in HOPS is seen to depend critically on interaction time and an Onset-time responsible for the same is demarcated.
The universe is believed to be originated from a quantum state. However, defining measurable quantities for the quantum properties in the present universe has gained interest recently. In this submission, we propose a quantum Poincare sphere as an observable quantity that can hint at the quantumness of primordial gravitational waves and large-scale magnetic fields. The Poincare sphere is defined in terms of quantum stokes operators associated with the polarization of those fields, which can be measured directly. We have further studied the effects of the initial non-BD vacuum on the power spec…
We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalise the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the non-classicality test with classical tomography methods based on the invers…
We introduce a general condition sufficient for the validity of the original Bell inequality (1964) in a local hidden variable (LHV) frame. This condition can be checked experimentally and incorporates only as a particular case the assumption on perfect correlations or anticorrelations usually argued for this inequality in the literature. Specifying this general condition for a quantum bipartite case, we introduce the whole class of bipartite quantum states, separable and nonseparable, that (i) admit an LHV description under any bipartite measurements with two settings per site; (ii) do not ne…
We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experime…
A state of a quantum systems can be regarded as {\it classical} ({\it quantum}) with respect to measurements of a set of canonical observables iff there exists (does not exist) a well defined, positive phase space distribution, the so called Galuber-Sudarshan $P$-representation. We derive a family of classicality criteria that require that averages of positive functions calculated using $P$-representation must be positive. For polynomial functions, these criteria are related to 17-th Hilbert's problem, and have physical meaning of generalized squeezing conditions; alternatively, they may be in…
Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the hypergraph $G$, and $|n \rangle$ denotes a binary vector of length $2^d$ with $1$ at $n$-th position for $n = 0, 1, \dots (2^d - 1)$. The non-classical properties of these states are studied. We consider annihilation and creation operator on the Hilbert space of dimension $2^d$ acting on the number states $\{|n \rangle: n = 0, 1, \dots (2^d - 1)\}$. The Hermiti…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has al…
One of the central foundational questions of physics is to identify what makes a system quantum as opposed to classical. One seminal notion of classicality of a quantum system is the existence of a non-contextual hidden variable model as introduced in the early work by Bell, Kochen and Specker. In quantum optics, the non-negativity of the Wigner function is a ubiquitous notion of classicality. In this work we establish an equivalence between these two concepts. In particular, we show that any non-contextual hidden variable model for Gaussian quantum optics has an alternative non-negative Wigne…
Astrophysical Graviton Squeezing Can Be Hidden in the Far-Field
Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）；School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学物理学院核物理与核技术国家重点实验室）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Beijing Laser Acceleration Innovation Center（北京激光加速创新中心）
Non-classical state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum non-demolition quadrature measurements and single quanta addition/subtraction to prepare quantum superposition states in bosonic systems. The performance of each permutation is quantified and compared using several different non-classicality criteria including Wigner negativity, non-classical depth, and optimal fidelity with a coherent state superposition. We also compare the p…
A sufficient condition for a quantum state of a system of spin-1/2 particles (spin-1/2s) to admit a local hidden variable (LHV) description i.e. to be classical is the separability of the density matrix characterizing its state, but not all classical states are separable. This leads one to infer that separability and classicality are two different concepts. These concepts are examined here in the framework of a criterion for identifying classicality of a system of spin-1/2s based on the concept of joint quasiprobability (JQP) for the eigevalues of spin components. The said criterion identifies…
We investigate the generation of non-classical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of non-classicality. We discuss…
We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakovsky inequalities. In this note some rigorous results on impossibility of classical hidden variables representations of certain quantum correlation functions are proved which are also based on the Cauchy-Bunyakovsky inequalities. The difference K between the variance and the mean as a measure of non-classicality of a state is discussed. For the classical case K is nonnegative while for the n-particle state i…
In a previous paper tests for entanglement for two mode systems involving identical massive bosons were obtained. In the present paper we consider sufficiency tests for EPR steering in such systems. We find that spin squeezing in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin variance test and squeezing in two mode quadratures all show that the quantum state is EPR steerable. We also find a generalisation of the Hillery-Zubairy planar spin variance test for EPR steering. The relation to previous correlation tests is discussed. This paper is based on a detailed classif…
We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more r…
