We investigate the violation of non-contextuality by a class of continuous variable states, including variations of entangled coherent states (ECS's) and a two-mode continuous superposition of coherent states. We generalise the Kochen-Specker (KS) inequality discussed in A. Cabello, Phys. Rev. Lett. 101, 210401 (2008) by using effective bidimensional observables implemented through physical operations acting on continuous variable states, in a way similar to an approach to the falsification of Bell-CHSH inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudo-spin observables and a generalized quasi-probability function.
We assess quantum non-locality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger (GHZ), W and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditions. This opens up the possibility for coherent exploitation of multipartite quantum channels made out of entangled thermal states. Our study is accompanied by a detailed description of possible generation schemes for the states analyzed.
We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH nonlocality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly nonclassical states of bosonic systems. [3]. However, Banaszek and Wódkiewicz later devised a phase-space approach based on the statistics gathered from the measurement of photon parity operators [4], demonstrating the key role played by non-Gaussianity in the revelation of the nonlocal feature of entangled two-mode states. This sort of approach finds its complement in nonlocality tests performed using Gaussian operations and measurements on non-Gaussian states, such as entangled coherent states (ECSs) [5], or de-Gaussified two-mode states achieved by resorting to photon subtraction (photon addition) [6][7][8][9][10]. On the other hand, recently it has been shown that the combination of Gaussian and nonGaussian measurements can lead to significant violations of local realistic models using continuous-variable systems [11,12].In particular, the nonlocal nature of an ECS has been extensively studied in past years, addressing tests based on effective pseudospin operators, photon parity operators, effective rotations, and dichotomized homodyne measurements, even in the presence of decoherence [13][14][15][16][17]. The latter approaches have been used for the violation of Bell-CHSH inequality [18] by states having a very large thermal occupation number [19], thus showing the possibility to reveal their nonclassical character, even under mechanisms that, naively, would be expected to wash out any quantumness. A conspicuous feature of ECS-based tests using homodyne measurements is that the violation of a Bell-CHSH inequality occurs only for coherent-state components having amplitude larger than a given threshold. Under realistic conditions, the threshold is typically determined by the operative conditions (detection inefficiencies and purity of the state resource, among other factors) under which the test is run. In light of the experimental difficulties encountered in the generation of ECS of largeamplitude components [20], it is clearly desirable to identify viable strategies for the falsification of local realistic theories with lower amplitude thresholds, so as to ease the experimental efforts required for such an important task.In this paper we report a test of local realism for ECS of light having an arbitrarily small amplitude, supplemented by the application of local noiseless amplification to the components of the system, after the implementation of the necessary local operations that are part of the Bell test [21,22]. By increasing the amplitude of the coherent-state componen...
Non-Markovian evolutions are responsible for a wide variety of physically interesting effects. Here, we study nonlocality of the nonclassical state of a system consisting of a qubit and an oscillator exposed to the effects of non-Markovian evolutions. We find that the different facets of non-Markovianity affect nonlocality in different and nonobvious ways, ranging from pronounced insensitivity of the Bell function to quite spectacular evidence of information kickback. In 1935, E. Schrödinger formulated a thought experiment addressing some paradoxical implications of the Copenhagen interpretation of quantum mechanics when pushed to the realm of everyday experience [1]. By describing a situation where the degrees of freedom of a "large" object are correlated in a quantum-mechanical way to a "small" quantum system, the paradox by Schrödinger (commonly referred to as the "cat paradox") embodies a genuine example of the possibility to enforce quantum features beyond the microscopic domain. Notwithstanding its almost octogenarian history, the cat paradox still defies a full understanding of its implications [2].The steady-pace experimental progress in quantum control achieved in the last 20 years has been able to produce instances very close to the original formulation by Schrödinger and is expected to help significantly in the grasping of fundamental concepts such as the quantum-to-classical transition, as well as the development of quantum technological applications [3]. States having the formwhere {|↑ s ,|↓ s } are the energy eigenstates of a spin-1/2 particle (a qubit) and |±D O are opposite-phase coherent states of a harmonic oscillator [4], are faithful instances of the situations envisaged in Ref. [1] and have been demonstrated in trapped-ion settings [3,5]. They are accessible (or close to be such) in other experimental contexts involving the effective interaction between spinlike systems and mechanical oscillators [6,7] or the all-optical generation of micro-macro states [8]. In the first instance, one would consider effective two-level systems (such as neutral or artificial atoms) embedded in cavities endowed with movable light mirrors [embodying the continuous-variable (CV) subsystem]. In the second one, the spin and CV parts are provided by different degrees of freedom of two distinct photonic information carriers. Both settings are able to engineer states having the form of Eq.(1) and both allow for the reconstruction of the Wigner function of the CV subsystem. As will be seen in the next section, such ability is crucial to the assessment of the Bell test at the core of our investigation. Remarkably, the multifaceted interests in studying quantum superposition states analogous to Eq. (1) extend up to the assessment of environment-induced dynamical effects and their implications for the settlement, manipulation, and protection of general quantum correlations. This is even more relevant when nontrivial environmental influences of a non-Markovian nature, such as those due to lack of divisibility dynamics and...
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