Related papers: Quasi-distributions for arbitrary non-commuting op…
Ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
Quantum key distribution, which allows two distant parties to share an unconditionally secure cryptographic key, promises to play an important role in the future of communication. For this reason such technique has attracted many…
The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…
In the article, on a new definition of quantum entropy, Campisi has explained an operator for entropy based on quantum number operator. It has been claimed that the expectation values for this operator increases for every non-quasi-static…
How to give a statistical description of thermodynamics in quantum systems is an open fundamental question. Concerning the work, the presence of initial quantum coherence in the energy basis can give rise to a quasiprobability of work,…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from…
We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter $\alpha$. This alternative simpler distribution…
A fundamental task in quantum information science is to transfer an unknown state from particle $A$ to particle $B$ (often in remote space locations) by using a bipartite quantum operation $\mathcal{E}^{AB}$. We suggest the power of…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schr\"odinger equation is also given. The dissipative and stochastic propagators are linked by the…
We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This…
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
We design a quasi-interpolation operator from the Sobolev space $H^1_0(\Omega)$ to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh with a computable approximation constant. The operator 1)…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…