Related papers: Unital Kadison-Schwarz Maps
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
Relativistic effects affect nearly all notions of quantum information theory. The vacuum behaves as a noisy channel, even if the detectors are perfect. The standard definition of a reduced density matrix fails for photon polarization…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
The capability to quantitatively distinguish quantum states is of great importance for a variety of tasks, and has recently played an important role in the study of quantum reduced dynamics and their characterization in terms of memory…
Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
Continuous-variable systems in quantum theory can be fully described through any one of the ${\rm s}$-ordered family of quasiprobabilities $\Lambda_{\rm s}(\alpha)$, ${\rm s} \in [-1,1]$. We ask for what values of $({\rm s}, a)$ is the…
It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon…
We analyze positivity of a tensor product of two linear qubit maps, $\Phi_1 \otimes \Phi_2$. Positivity of maps $\Phi_1$ and $\Phi_2$ is a necessary but not a sufficient condition for positivity of $\Phi_1 \otimes \Phi_2$. We find a…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…
In this work, we adapt Sinkhorn-Knopp theorem for rectangular positive maps $(T:M_k\rightarrow M_m)$. We extend their concepts of support and total support to these maps. We show that a positive map $T:M_k\rightarrow M_m$ is equivalent to a…
The unknown state $\hrho$ of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix $\hrho$ and the…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…