Related papers: Equivalence of Quantum States under Local Unitary …
We derive necessary and sufficient conditions for the LU-equivalence of two general (pure or mixed) $n$-qubit states as well as we determine the local unitary operators connecting them. Almost all relevant information is contained in the…
We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords…
In this paper, we consider the local unitary classification of the class of qudit bipartite mixed states for which no information can be obtained locally. These states are represented by symmetrical density matrices in which both tracial…
In the present paper few steps are undertaken towards the description of the qubit-qutrit pair - quantum bipartite system composed of two and three level subsystems. The computational difficulties with the construction of the local unitary…
We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state $|\Psi>>=\sum_{ij} \psi_{ij}\: |i>_1\otimes |j>_2$ the complete characterization of the class of local unitaries $U_1\otimes U_2$ for which…
Research on quantum states often focuses on the correlation between nonlocal effects and local unitary invariants, among which local unitary equivalence plays a significant role in quantum state classification and resource theories. This…
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…
The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
We derive necessary and sufficient conditions for local unitary (LU) operators to leave invariant the set of 1-qubit reduced density matrices of a multi-qubit state. LU operators with this property are tensor products of {\it cyclic local}…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way…
The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally…
We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the…
Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under…
We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed…
We refine recent local unitary entanglement classification for symmetric pure states of $n$ qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer…
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…