Related papers: Local Unitary Invariants for N-qubit Pure State
Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N- qubit state and linear entropy of reduced single qubit…
Local unitary invariance and the notion of negativity fonts are used as the principle tools to construct four qubit invariants of degree 8, 12, and 24. A degree 8 polynomial invariant that is non-zero on pure four qubit states with…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…
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…
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if…
The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different…
A new form of local unitary (LU) transformation invariant is given for multi-qubit states . The general relation between tangle and the LU transformation invariant of pure three and four-qubit states is given. We find that the tangle…
We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…
A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher…
We present a complete set of local unitary invariants for generic multi-qubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in…
Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two…
We present two general methods to implement quantum circuits for the direct measuring of local unitary invariants on quantum computers. We work these out for important three-qubit invariants, and also demonstrate these on the IBM Quantum…
Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure…
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 local unitary equivalence for two and three-qubit mixed states by investigating the invariants under local unitary transformations. For two-qubit system, we prove that the determination of the local unitary equivalence of…
The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
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…