The Independence of Distinguishability and the Dimension of the System
arXiv:2010.03120 · doi:10.1007/s10773-022-05127-5
Abstract
The are substantial studies on distinguishabilities, especially local distinguishability, of quantum states. It is shown that a necessary condition of a local distinguishable state set is the total Schmidt rank not larger than the system dimension. However, if we view states in a larger system, the restriction will be invalid. Hence, a nature problem is that can indistinguishable states become distinguishable by viewing them in a larger system without employing extra resources. In this paper, we consider this problem for (perfect or unambiguous) LOCC, PPT and SEP distinguishabilities. We demonstrate that if a set of states is indistinguishable in , then it is indistinguishable even being viewed in , where are integers. This shows that such distinguishabilities are properties of states themselves and independent of the dimension of quantum system. Our result gives the maximal numbers of LOCC distinguishable states and can be employed to construct a LOCC indistinguishable product basis in general systems. Our result is suitable for general states in general systems. For further discussions, we define the local-global indistinguishable property and present a conjecture.
arXiv comment10 pages
References in corpus (30)
- Quantum Nonlocality without Entanglement
- Unextendible Product Bases and Bound Entanglement
- Local Distinguishability of Multipartite Orthogonal Quantum States
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Distinguishability of the Bell states
- Distinguishability and indistinguishability by LOCC
- Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
- Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
- Distinguishability of maximally entangled states
- Optimal distinction between non-orthogonal quantum states
- Nonlocality of orthogonal product basis quantum states
- Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
- Distinguishability of complete and unextendible product bases
- Understanding entanglement as resource: locally distinguishing unextendible product bases
- Local indistinguishability of orthogonal product states
- Condition for unambiguous state discrimination with local operations and classical communication
- Three maximally entangled states can require two-way LOCC for local discrimination
- Unambiguous Discrimination Between Linearly Dependent States with Multiple Copies
- Entanglement as a resource for local state discrimination in multipartite systems
- Distinguishing a set of full product bases needs only projective measurements and classical communication
- Local Distinguishability of Any Three Quantum States
- Asymptotically perfect discrimination in the LOCC paradigm
- Orthogonality And Distinguishability: Criterion For Local Distinguishability of Arbitrary Orthogonal States
- Optimal resource states for local state discrimination
- The local distinguishability of any three generalized Bell states
- On small set of one-way LOCC indistinguishability of maximally entangled states
- Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource
- Framework for distinguishability of orthogonal bipartite states by one-way local operations and classical communication
- LOCC distinguishable orthogonal product states with least entanglement resource