Related papers: Unital Positive Maps and Quantum States
A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts…
We construct a new class of PPT states for bipartite "d x d" systems. This class is invariant under the maximal commutative subgroup of U(d) and contains as special cases almost all known examples of PPT states. Theses states may be used to…
The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of…
We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we…
We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4x4 bipartite system.
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial…
We construct the positive invertible map of the mixed states of a single qutrit onto the states of two identical fermions. It is shown that using this one-to-one correspondence between qutrit states and states of two identical…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…
The physically allowed quantum evolutions on a single qubit can be described in terms of their geometry. From a simple parameterisation of unital single-qubit channels, the canonical form of all such channels can be given. The related…
The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without…
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…
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various…