Related papers: Operational quasiprobabilities for continuous vari…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
Many situations in quantum theory and other areas of physics lead to quasi-probabilities which seem to be physically useful but can be negative. The interpretation of such objects is not at all clear. In this paper, we show that…
Teleportation of optical field states (as continuous quantum variables) is usually described in terms of Wigner functions. This is in marked contrast to the theoretical treatment of teleportation of qubits. In this paper we show that by…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
An experimental comparison of several operational phase concepts is presented. In particular, it is shown that statistically motivated evaluation of experimental data may lead to a significant improvement in phase fitting upon the…
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov's weak value, from which the QP can be defined…
Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system's…
A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the…
We propose and investigate an optical scheme for probabilistic implementation of an arbitrary single-mode quantum operation that can be expressed as a function of photon number operator. The scheme coherently combines multiple photon…
We formulate incomplete classical statistics for situations where the knowledge about the probability distribution outside a local region is limited. The information needed to compute expectation values of local observables can be collected…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…