2013/10/25 by Samuel R. Hedemann, Hedemann, Samuel R. · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1310.7038
21 pages 9 figures. v2: Term "local-unitary" replaced by "entanglement-preserving unitary" (EPU) since product-form not nec. to preserve X-state entanglement. v3: Formally defined EPU, added proof for rank-2 family and Appendix proving EPUs can be nonloc. for X states, and EPU-rotated X states have enough DOF for gen. mixed states. v4: Success on 10,000 consecutive states. Basic results unchanged
openalex publication_date 2013/10/25 · arxiv created 2014/08/07 · arxiv updated 2014/08/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Strong numerical evidence is presented suggesting that all two-qubit mixed states are equivalent to X states by a single entanglement-preserving unitary (EPU) transformation, so that the concurrence of such an X state equals that of the original general state. An X-state parameterization of a general two-qubit state is given, allowing all states to have their concurrence parametrically specified. A new kind of entanglement measure is proposed, relating a general state's entanglement to that of a pure state in the same system. New states called "H States" are presented, having fully parametric concurrence and purity, with the intention of using them to construct entanglement-preserving depolarization channels, which may aid development of the new entanglement measure. A theory of "true-generalized" X states (TGX states) is proposed for the general case of N-partite systems. While such states do not generally have the literal "X" shape, evidence is shown that they are the true generalizations of X states in larger systems, since they appear to always be EPU-equivalent to general states of all ranks, whereas literal X states generally are not. An example of this is given for 2× 3, including the proposition of the 2× 3 maximally entangled mixed states (MEMS). If the claim that TGX states are universal is valid, then any entanglement measure may be computable in a simpler form by using the EPU-equivalence between general states and TGX states.