# Local unitary equivalence of multipartite pure states.

@article{Kraus2010LocalUE, title={Local unitary equivalence of multipartite pure states.}, author={Barbara Kraus}, journal={Physical review letters}, year={2010}, volume={104 2}, pages={ 020504 } }

Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under local unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU equivalent iff their standard forms coincide. The LU-equivalence problem for nongeneric states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.

## 73 Citations

Criterion of Local Unitary Equivalence for Multipartite States

- Physics, Mathematics
- 2013

We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general…

Classification of arbitrary multipartite entangled states under local unitary equivalence

- Physics
- 2013

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…

A Note on Local Unitary Equivalence of Isotropic-like States

- Mathematics
- 2015

We consider the local unitary equivalence of a class of quantum states in bipartite case and multipartite case. The necessary and sufficient condition is presented. As special cases, the local…

Local Unitary Invariants for Multipartite States

- Mathematics
- 2013

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…

How many invariant polynomials are needed to decide local unitary equivalence of qubit states

- Mathematics
- 2013

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…

Unitary equivalence of different bipartite entangled states under unitary transformations

- Physics
- 2014

On Local Unitary Equivalence of Two and Three-qubit States

- Mathematics, PhysicsScientific Reports
- 2017

It is proven that the determination of the local unitary equivalence of 2-qubits states only needs 14 or less invariants for arbitrary two-qubit states, and it is proved that these invariants are sufficient to guarantee the LU equivalences of certain kind of three-qu bit states.

Locally inequivalent four-qubit hypergraph states

- Physics
- 2014

Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizers. Using local Pauli equivalence and permutational symmetry, we reduce the 32…

Local unitary equivalence of the SLOCC class of three qubits

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

Classification of multipartite pure states via the local unitary (LU) equivalence or the stochastic local operations and classical communication (SLOCC) equivalence is a fundamental task in…

A note on state decomposition independent local invariants

- Mathematics
- 2013

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…