Related papers: Complete Separability and Fourier representations …
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
Compatibility conditions between the (global) spectrum of an $n$-mode Gaussian state and the spectra of the individual modes are presented, making optimal use of beam splitter and (two-mode) squeezing transformations. An unexpected…
In this note a very crude but simple approximation to the set of separable states in an arbitrary simplex of commutative states is given using the fact that on the lines connecting the maximally mixed state and an arbitrary pure state the…
By focusing on the X-matrix part of a density matrix of two qubits we provide an algebraic lower bound for the concurrence. The lower bound is generalized for cases beyond two qubits and can serve as a sufficient condition for…
We present a general methodology to obtain the basis of qudits which are admissible to Quantum Fourier Transform (QFT). We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for…
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…
The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric…
Properties of group coherent states can be derived "effectively" without knowing full wave functions. The procedure is detailed in this article as an example of general methods for effective constraints. The role of constraints in the…
We introduce a nonsymmetric real matrix which contains all the information that the usual Hermitian density matrix does, and which has exactly the same tensor product structure. The properties of this matrix are analyzed in detail in the…
We discuss the critical point $x_c$ separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator $\rho=x|\tilde{\phi}><\tilde{\phi}| + \frac{1-x}{D^N}…
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
We investigate the separability properties of quantum states described by an extended Werner density matrix, where the classical component exhibits statistical dependence. By generalizing the classical part to allow correlations, we…
Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was…
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…
In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is…
If a pure state of a qubit pair is developed over the four basis states, it is known that an equality between the four coefficients of that development exists if and only if that state is unentangled. This paper considers an arbitrary pure…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…