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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…
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 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 investigate the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for fixed numbers of qubits. We explicitly exhibit the homomorphism between complex and real groups for two-qubits,…
Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively…
We define a square matrices, by which some stochastic local operations and classical communication (SLOCC) invariants can be obtained. The relation of SLOCC invariants and character polynomial of square matrix are given for three and four…
Characterization and quantification of multipartite entanglement is one of the challenges in state-of-the-art experiments in quantum information processing. According to theory, this is achieved via entanglement monotones, that is,…
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 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…
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 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…
We proposed a concept of LU transformation invariant operators. By using this operator, arbitrary multi-qubit states LU transformation invariant and SLOCC invariant could be easily obtained. And we find that presences two kinds of invariant…
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…
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…
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 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…
Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by…
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…
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…
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…