Related papers: Quantum states with strong positive partial transp…
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that this is true in most cases if the number of product vectors is…
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…
Higher-dimensional quantum systems are attracting interest for improving quantum protocol performance by increasing memory space. Characterizing quantum resources of such systems is fundamental but experimentally costly. We tackle the first…
We consider the transformation of multi-partite states in the single copy setting under positive-partial-transpose-preserving operations (PPT-operations) and obtain both qualitative and quantitative results. Firstly, for some pure state…
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit…
In this paper, we mainly discuss the separability of $n$-partite quantum states from elements of density matrices. Practical separability criteria for different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some of them…
Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying…
Power symmetric matrices defned and studied by R. Sinkhorn (1981) and their generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have been utilized to give positive block matrices with trace one possessing positive…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
Multiqubit positive-partial-transpose (PPT) entangled states play an important role in quantum information theory. We characterize such states of minimum rank in three-qubit system, namely rank four. Depending on whether the Lorentz…
We show that any bipartite quantum state of rank four is distillable, when the partial transpose of the state has at least one negative eigenvalue, i.e., the state is NPT. For this purpose we prove that if the partial transpose of a…
Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition,…
Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems…
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…
We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is…
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of…
We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of…
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…