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Elena R. Loubenets

Publications and source records attributed to Elena R. Loubenets.

42 records · Page 3Linked to original sources
arXiv2004

On validity of the original Bell inequality for the Werner nonseparable state

In quant-ph/0406139, we have introduced in a very general setting the new class of quantum states, density source-operator states, satisfying any classical CHSH-form inequality, and shown that any separable state belongs to this class. In the present paper, we prove that the Werner nonseparable state also belongs to the class of density source-operator states. Moreover, for any dimension d>2, the Werner state is in such a subclass of this class where each density source-operator state satisfies also the perfect correlation form of the original Bell inequality regardless of whether or not the Bell perfect correlation restriction is fulfilled. The latter earlier unknown property of the Werner state can be verified experimentally.

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arXiv2003

General framework for the probabilistic description of experiments

We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized observable, this framework allows us to subsume different types of randomness and experiment effects within a single mathematical structure. Adjusting this framework to the quantum case, we clarify what is really "quantum" in quantum measurement theory.

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arXiv2003

On separability of quantum states and the violation of Bell-type inequalities

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system in a separable state. We derive quantum analogues of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended CHSH inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.

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arXiv2003

General Probabilistic Framework of Randomness

We introduce a new mathematical framework for the probabilistic description of an experiment upon a system of any type in terms of initial information representing this system. Based on the notions of an information state, an information state space and a generalized observable, this general framework covers the description of a wide range of experimental situations including those where, with respect to a system, an experiment is perturbing. We prove that, to any experiment upon a system, there corresponds a unique generalized observable on a system initial information state space, which defines the probability distribution of outcomes under this experiment. We specify the case where initial information on a system provides "no knowledge" for the description of an experiment. Incorporating in a uniform way the basic notions of conventional probability theory and the non-commutativity aspects and the basic notions of quantum measurement theory, our framework clarifies the principle difference between Kolmogorov's model in probability theory and the statistical model of quantum theory. Both models are included into our framework as particular cases. We show that the phenomenon of "reduction" of a system initial information state is inherent, in general, to any non-destructive experiment and upon a system of any type. Based on our general framework, we introduce the probabilistic model for the description of non-destructive experiments upon a quantum system and prove that positive bounded linear mappings on the Banach space of trace class operators, arising in the description of experiments upon a quantum system, are completely positive.

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arXiv2001

Quantum stochastic approach to the description of quantum measurements

In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a possible integral representation of an instrument, which differs from the representations of an instrument available in the mathematical and physical literature. We introduce the notion of a quantum stochastic representation of an instrument, whose elements are wholly determined by the unitary invariants of a measuring process. We show that the description of a generalized direct quantum measurement can be considered in the frame of a new general approach, which we call the quantum stochastic approach (QSA), based on the notion of a family of quantum stochastic evolution operators, satisfying the orthonormality relation and describing the conditional evolution of a quantum system under a measurement. The QSA allows to give: a) the complete statistical description of any generalized direct quantum measurement (a POV measure and a family of posterior states); b) the complete description in a Hilbert space of the stochastic behaviour of a quantum system under a measurement in the sense of specification of the probabilistic transition law governing the change from the initial state of a quantum system to a final one under a single measurement; c) to formalize the consideration of all possible types of quantum measurements. For measurements continuous in time the QSA allows, in particular, to define in the most general case (without assuming any Markov property) the notion of posterior pure state trajectories (quantum trajectories) and to give their probabilistic treatment.

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