Related papers: Convex set of quantum states with positive partial…

For a system of N identical particles in a random pure state, there is a threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each typically share entanglement if k > k_0, and typically do not share entanglement if k < k_0.…

Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…

We construct a large class of quantum "d x d" states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic…

We construct a large class of bipartite M x N quantum states which defines a proper subset of states with positive partial transposes (PPT). Any state from this class is PPT but the positivity of its partial transposition is recognized with…

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

We study the general representations of positive partial transpose (PPT) states in ${\cal C}^K \otimes {\cal C}^M \otimes {\cal C}^N$. For the PPT states with rank-$N$ a canonical form is obtained, from which a sufficient separability…

We express the positive partial transpose (PPT) separability criterion for symmetric states of multi-qubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix…

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…

In this paper, we first obtain an algebraic formula for the moments of a centered Wishart matrix, and apply it to obtain new convergence results in the large dimension limit when both parameters of the distribution tend to infinity at…

It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…

The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…

We report here on the results of numerical searches for PPT states with specified ranks for density matrices and their partial transpose. The study includes several bipartite quantum systems of low dimensions. For a series of ranks extremal…

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…

Let W be a Wishart random matrix of size d^2 times d^2, considered as a block matrix with d times d blocks. Let Y be the matrix obtained by transposing each block of W. We prove that the empirical eigenvalue distribution of Y approaches a…

We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…

Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance…

We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical…

We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the…

We analyze a class of positive partial transpose states (PPT) such that the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator (Cholesky block decomposition). We…

A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…