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We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form $W=rho-c_{rho} I$, where $rho$ is a density matrix, $c_{rho}$ is a non-negative number related to $rho$, and $I$ is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamio{l}kowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provide the necessary and sufficient condition of the entanglement witness $W=rho-c_{rho}I$ in operation, as well as in theory.
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction provides na
The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled
Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the inertias of EWs, i.e., the triplet of the numbers of negative, zero, and positive eigenvalues respectively. We focus on the EWs constructed by the par
An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the (upper) bou
Let $mathscr{H}$ be a finite-dimensional complex Hilbert space and $mathscr{D}$ the set of density matrices on $mathscr{H}$, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure $u$ on $mathscr{D}$ tha