Related papers: Conditions for uniqueness of product representatio…
Separability of quantum states is analyzed with the use of the Choi-Jamiolkowski isomorphism. Spectral separability criteria are derived. The presented approach is illustrated with various examples, among which a separable decomposition of…
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…
Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in…
Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski…
We define a product between quantum superoperators which is preserved under the Choi-Jamio{\l}kowski-Kraus-Sudarshan channel-state isomorphism. We then identify the product as the convolution on the space of superoperators, with respect to…
Product states are always considered as the states that don't contain quantum correlation. We discuss here when a quantum channel sends the product states to themselves. The exact forms of such channels are proposed. It is shown that such a…
We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…
A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained. This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
We introduce and study the notion of steerability for channels. This generalizes the notion of steerability of bipartite quantum states. We discuss a key conceptual difference between the case of states and the case of channels: while state…
A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional…
We investigate the coherence of quantum channels using the Choi-Jamio\l{}kowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when…
A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under…
In quantum information, most information processing processes involve quantum channels. One manifestation of a quantum channel is quantum operation acting on quantum states. The coherence of quantum operations can be considered as a quantum…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamio{\l}kowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae and we…
A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with…
We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary…
We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An…