Related papers: Purity distribution for bipartite random pure stat…
We conduct quasi-Monte Carlo numerical integrations in two very high (80 and 79)-dimensional domains -- the parameter spaces of rank-9 and rank-8 qutrit-qutrit (9 x 9) density matrices. We, then, estimate the ratio of the probability -- in…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
We present a general method for constructing pure-product-state representations for density operators of $N$ quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the…
We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…
Based on a general unitary operation of two-qubit system, we investigate the dynamics of entanglement, entropy and purity. Distinctive features in the different initial states settings of an interacting bipartite system are explored. The…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an…
We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations) any state chosen from the set of…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
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…
Compelling evidence-though yet no formal proof-has been adduced that the probability that a generic (standard) two-qubit state ($\rho$) is separable/disentangled is $\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723).…
It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a…
Local pure states are an important resource for quantum computing. The problem of distilling local pure states from mixed ones can be cast in an information theoretic paradigm. The bipartite version of this problem where local purity must…
A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special…
New inequalities for tomographic probability distributions and density matrices of qutrit states are obtained by means of generalization of qubit portrait method. The approach based on the qudit portrait method to get new entropic…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking…
We study exact local compression of a quantum bipartite state; that is, applying local quantum operations to reduce the dimensions of the Hilbert spaces while perfectly preserving the correlation. We provide a closed-form expression for the…