Related papers: A Simple Set of Separable States in a Commutative …
The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average entanglement of an ensemble of pure…
Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…
For configurational space of arbitrary dimension a strict form of the uncertainty principle has been obtained, which takes into account the dependence of inequality limit on the effective number of pure states present in given statistical…
In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…
This research introduces the concept of the purity number, which represents the number of separable s-particle sub-states within an n-particle state ($s<n$ ). It establishes that, for any , achieving the maximum purity number is both a…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
We construct a family of bipartite states of arbitrary dimension whose eigenvalues of the partially transposed matrix can be inferred directly from the block structure of the global density matrix. We identify from this several subfamilies…
Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying…
We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…
We study the closest disentangled state to a given entangled state in any system (multi-party with any dimension). We obtain the set of equations the closest disentangled state must satisfy, and show that its reduction is strongly related…
We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is…
In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way…
We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical…
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…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…
In this paper, based on a matrix norm, we first present a ball of separable unnormalized states around the identity matrix for the bipartite quantum system, which is larger than the separable ball in Frobenius norm. Then the proposed ball…
Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also…
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…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
We give a simple and efficient process for generating a quantum superposition of states which form a discrete approximation of any efficiently integrable (such as log concave) probability density functions.