Related papers: Positivity and complete positivity of differentiab…
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme…
It is a well-known result due to E. St{\o}rmer that every positive qubit map is decomposable into a sum of a completely positive map and a completely copositive map. Here, we generalize this result to tensor squares of qubit maps.…
Open quantum dynamics in a tripartite scenario including a system, its environment and a passive reference is shown to resolve several open questions regarding not completely positive (NCP) dynamical maps as valid descriptions of open…
We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and…
A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We…
The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment…
Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
The recently introduced CP*-construction unites quantum channels and classical systems, subsuming the earlier CPM-construction in categorical quantum mechanics. We compare this construction to two earlier attempts at solving this problem:…
We analyze the geometry of positive and completely positive, trace preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and non-invertible Pauli channels. Using the…
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are…
We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family of inner products, also providing new information on the order strucure an extreme points in some…
We address the problem of finding optimal CPTP (completely positive, trace preserving) maps between a set of binary pure states and another set of binary generic mixed state in a two dimensional space. The necessary and sufficient…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process…
In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates,…
We show that all $2\otimes 4$ states with strong positive partial transposes (SPPT) are separable. We also construct a family of $2\otimes 5$ entangled SPPT states, so the conjecture on the separability of SPPT states are completely…
Divisible dynamical maps play an important role in characterizing Markovianity on the level of quantum evolution. Divisible maps provide important generalization of Markovian semigroups. Usually one analyzes either completely positive or…