Related papers: Hilbert's 17th problem and the quantumness of stat…
We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To…
Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of $d$-dimensional quantum states of…
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence…
We provide experimental evidence of quantum features in bi-partite states classified as entirely classical according to a conventional criterion based on the Glauber P-function but possessing non-zero Gaussian quantum discord. Their quantum…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multi-mode Gaussian states has posed some…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The problem of quantum state reduction in the process of measurement has attracted attention of almost everyone who created, developed or explained quantum physics to the students. Absence of a solution is the basis for the statement that…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…