相关论文: Distinguishing separable and entangled states

We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation…

We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose (PPT) criterion and formulate a Horodecki-type Theorem.

Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…

In this paper, a class of indecomposable positive finite rank elementary operators of order $(n,n)$ are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of…

We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…

Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound…

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…

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled…

A key requirement of any separable quantum state is that its density matrix has a positive partial transpose. For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose…

We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…

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…

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, where the positive partial transpose…

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the…

A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…

We revisit the criterion of multi-particle entanglement based on the overlaps of a given quantum state $\rho$ with maximally entangled states. For a system of $m$ particles, each with $N$ distinct states, we prove that $\rho$ is…

We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of $m$ vs $n$…

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…

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…

Bound entangled (BE) states are strange in nature: non-zero amount of free entanglement is required to create them but no free entanglement can be distilled from them under local operations and classical communication (LOCC). Even though…