Related papers: Local unitary invariants for multipartite states
Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…
Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure…
From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are…
Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…
We show that the quantum discord and the measurement induced non-locality (MiN) in a bipartite quantum state is invariant under the action of a local quantum channel if and only if the channel is invertible. In particular, these quantities…
We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We…
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…
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…
We propose to characterize multipartite entanglement of pure states as local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a definition of…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness. This paper systematically investigates the characteristics of bipartite and multipartite quantum states…
We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both…
In this paper we study local unitary invariants of a multi-partite quantum state that are monotonic, on average, under local operations and classical communication (locc). In particular we focus on local unitary invariants that are…
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 degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…
It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states.…
The classification of multipartite entanglement is essential as it serves as a resource for various quantum information processing tasks. This study concerns a particular class of highly entangled multipartite states, the so-called…
We propose a new kind of invariant of multi-party stabilizer states with respect to local Clifford equivalence. These homological invariants are discrete entities defined in terms of the entanglement a state enjoys with respect to arbitrary…
We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. The necessary and sufficient conditions under which a mean field state…
Mixed states that are uniquely determined among all (UDA) states are vital in efficient quantum tomography. We show the necessary and sufficient conditions by which some multipartite mixed states are UDA by their $k$-partite reduced density…