Related papers: All unitaries having operator Schmidt rank 2 are c…
A definition of the Schmidt number of a state of an infinite dimensional bipartite quantum system is given and properties of the corresponding family of Schmidt classes are considered. The existence of states with a given Schmidt number…
Efficient verification of quantum states and gates is crucial to the development of quantum technologies. Although the sample complexities of quantum state verification and quantum gate verification have been studied by many researchers,…
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitaries play a relevant role.…
We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al., which show that in large d x…
Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. Schmidt number is a quantity on the entanglement dimension of a bipartite state. Here we build families of k-positive maps from…
A set of all states of a bi-partite quantum system can be divided into subsets each of which contains states with the same degree of entanglement. In this paper we address a question whether local operations (without classical…
We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…
We discuss the monotonicity under local operations and classical communication (LOCC) of systematically constructed quantities aiming at quantification of entanglement properties of multipartite quantum systems. The so-called generalized…
We investigate how originally localized two pieces of quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization…
The general class of Gaussian Schmidt-number witness operators for bipartite systems is studied. It is shown that any member of this class is reducible to a convex combination of two types of Gaussian operators using local operations and…
We introduce two operational entanglement measures which are applicable for arbitrary multipartite (pure or mixed) states. One of them characterizes the potentiality of a state to generate other states via local operations assisted by…
Nielsen characterized in full those 2-party quantum protocols of local operations and classical communication that transform, with probability one, a pure global initial state into a pure global final state. The present work considers the…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
By exploiting the permutation symmetry of Dick states, we derive closed analytical expressions of Schmidt decompositions for {\it all} possible bipartitions of a system described by this kind of state. This allows us to exhaustively compute…
We conjecture analytic expressions for the non-local magic of bipartite pure qudit states of prime local dimension. Our construction relies on the Schmidt-aligned state attaining the minimum over local unitaries, a hypothesis that we…
Some progress is reported on conditions for convertibility among bipartite 2x2 entangled states: An inconvertibility condition related to the rank of an entangled state is given that it is impossible to convert to an entangled state with…
Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of…
We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated…
We study Schmidt rank for a vector (i.e., a pure state) and Schmidt number for a mixed state which are entanglement measures. We show that if a subspace of a certain bipartite system contains no vector of Schmidt rank $\leqslant k$, then…
We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that…