Related papers: A classification of incomparable states
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the GHZ-class and the W-class. Any two states within the same class can be transformed into…
Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical…
Multipartite quantum entanglement serves as a resource for spatially separated parties performing distributed quantum information processing. Any multipartite entangled state can be generated from appropriately distributed bipartite…
We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \leq d$ orthogonal maximally entangled states in…
We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
More than two multipartite orthogonal states cannot always be discriminated (with certainty) if only local operations and classical communication (LOCC) are allowed. Using an existing inequality among the measures of entanglement, we show…
A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a…
Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. A set of quantum states is said to admit state exclusion if there exists a measurement whose…
We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
We investigate the relationship between locally maximally entangleable (LME) states and W-type states which are equivalent to a W state under stochastic local operations and classical communication (SLOCC). We prove that (i) some special…
The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to…
Entanglement is a resource in quantum information theory when state manipulation is restricted to Local Operations assisted by Classical Communication (LOCC). It is therefore of paramount importance to decide which LOCC transformations are…
Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be…
We consider the problem of local operations and classical communication (LOCC) discrimination between two bipartite pure states of fermionic systems. We show that, contrary to the case of quantum systems, for fermionic systems it is…
It is a well known fact that an quantum state $|\psi(\theta,\phi)>$ is represented by a point on the Bloch sphere, characterized by two parameters $\theta$ and $\phi$. In a recent work we already proved that it is impossible to partially…
Suppose two distant observers Alice and Bob share a pure biparticle entangled state secretly chosen from a set, it is shown that Alice (Bob) can probabilistic concentrate the state to a maximally entangled state by applying local operations…