Abstract

In this paper the local distinguishability of generalized Bell states in arbitrary dimension is investigated. We firstly study the decomposition of a basis which consists of d 2 number of generalized Pauli matrices. We discover that this basis is equal to the union of D number of different sets, where and ϕ is Euler ϕ-function. Then we define the generator of the matrices in this decomposition, and exhibit an algorithm to calculate generators of a given set of matrices. This algorithm shows that generators of a given set can be calculated simply and efficiently. Secondly, we show that a set of GBSs can be distinguished by one-way LOCC if the cardinality of is less than Dϕ(d), where is a set of generators of all the elements in difference set of a set of GBSs. The previous results in [2004 Phys. Rev. Lett. 92 177905; 2019 Phys. Rev. A 99 022307; 2021 Quantum Inf. Process. 20 52] can be covered by our result. Finally, for the uncovered cases in [2021 Quantum Inf. Process. 20 52], we give a new result to partly solve that problem.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call