Related papers: Quantum conditional operator and a criterion for s…
This paper presents some of the basic properties of conditioned observables in finite-dimensional quantum mechanics. We begin by defining the sequential product of quantum effects and use this to define the sequential product of two…
We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…
In any bipartition of a quantum state, it is proved that the negative values of the conditional version of sandwiched Tsallis relative entropy necessarily implies quantum entanglement. For any N, the separability ranges in the $1:N-1$…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix…
Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
Necessary and sufficient conditions for the existence of a composite-system statistical operator, and, separately, for the possibility of its being correlated or uncorrelated, are derived in terms of its range dimension and the range…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
We introduce and explore two questions concerning spectra of operators that are of interest in the theory of entanglement in symmetric (i.e., bosonic) quantum systems. First, we investigate the inverse eigenvalue problem for symmetric…
We consider the operator $${\cal H} = {\cal H}' -\frac{\partial^2\ }{\partial x_d^2} \quad\text{on}\quad\omega\times\mathbb{R}$$ subject to the Dirichlet or Robin condition, where a domain $\omega\subseteq\mathbb{R}^{d-1}$ is bounded or…
Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator.…
Nonseparability - multipartite states that cannot be factorized - is one of the most striking features of quantum mechanics, as it gives rise to entanglement and non-causal correlations. In quantum computing, it also contributes directly to…
Separability from the spectrum is a significant and ongoing research topic in quantum entanglement. In this study, we investigate properties related to absolute separability from the spectrum in qudits-qudits states in the bipartite states…