A Note on State Decomposition Independent Local Invariants
Ting-Gui Zhang, Naihuan Jing, Xianqing Li-Jost, Ming-Jing Zhao,, Shao-Ming Fei
TL;DR
This paper introduces a set of local unitary invariants for quantum systems, based on hyperdeterminants, which do not depend on state decompositions and help determine state equivalence.
Contribution
It presents a novel method to derive invariants for quantum states that are independent of pure state decompositions, aiding in state classification.
Findings
Invariants are expressed via hyperdeterminants.
Invariants provide necessary conditions for state equivalence.
Applicable to arbitrary dimensional quantum systems.
Abstract
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 state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.