Using Partial Transpose and Realignment to generate Local Unitary Invariants
arXiv:1301.4082 · doi:10.1103/PhysRevA.87.052311
Abstract
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}, 062308 (2011)]. This paper first points the equivalence of the so constructed transformations to the combined operations of partial transpose and realignment. This allows construction of local unitary invariants of any system, with subsystems of arbitrary dimensions. Some properties of the resulting operators and consequences for pure tripartite higher dimensional states are briefly discussed.
arXiv comment5 pages, 2 figures
References in corpus (19)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement of a Pair of Quantum Bits
- Distributed Entanglement
- The logarithmic negativity: A full entanglement monotone that is not convex
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- On the role of entanglement in quantum computational speed-up
- Entangled Quantum States of Magnetic Dipoles
- Multi-particle entanglement and its applications to cryptography
- Some Properties of the Computable Cross Norm Criterion for Separability
- Computing Local Invariants of Qubit Systems
- All entangled states are useful for channel discrimination
- Entangling power of quantized chaotic systems
- On multi-particle entanglement
- Geometric local invariants and pure three-qubit states
- All degree six local unitary invariants of k qudits
Cited by in corpus (5)
- Diagonal unitary entangling gates and contradiagonal quantum states
- Partial transpose criteria for symmetric states
- Criterion of Local Unitary Equivalence for Multipartite States
- Simple permutation-based measure of quantum correlations and maximally-3-tangled states
- Local Unitary Invariants for Multipartite Quantum Systems