Related papers: Locally undetermined states, generalized Schmidt d…
We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case,…
We show that almost every pure state of multi-party quantum systems (each of whose local Hilbert space has the same dimension) is completely determined by the state's reduced density matrices of a fraction of the parties; this fraction is…
In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite…
We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta =1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $| \psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha \beta})$ is…
A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are…
A set of quantum states is said to be antidistinguishable if, upon being given a randomly chosen state, it is possible to identify a state that the system was definitively not prepared in. In this work, we begin with a study of quantum…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
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…
Recent findings suggest, separable states, which are otherwise of no use in entanglement dependent tasks, can also be used in information processing tasks that depend upon the discord type general non classical correlations. In this work,…
Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is…
Generic high-dimensional bipartite pure states are overwhelmingly likely to be highly entangled. Remarkably, this ubiquitous phenomenon can already arise in finite-dimensional systems. However, unlike the bipartite setting, the entanglement…
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of…
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that the correlations observed for some entangled quantum states can be explained…
We consider one copy of a quantum system prepared in one of two orthogonal pure states, entangled or otherwise, and distributed between any number of parties. We demonstrate that it is possible to identify which of these two states the…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…