In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality in multipartite quantum systems. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving positive operator-valued measures on fixed subsystem and partially answer an open question given by Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. The connection between the nonlocality and the plane structure of OPSs is established. We successfully construct a strongly nonlocal OPS in ${\mathcal{C}}^{{d}_{A}}\ensuremath{\bigotimes}{\mathcal{C}}^{{d}_{B}}\ensuremath{\bigotimes}{\mathcal{C}}^{{d}_{C}}\phantom{\rule{4pt}{0ex}}({d}_{A},{d}_{B},{d}_{C}\ensuremath{\ge}4)$, which contains fewer quantum states, and generalize the structures of known OPSs to any possible three and four-partite systems. In addition, we propose several entanglement-assisted protocols for perfectly local discrimination of the sets. It is shown that the protocols without teleportation use less entanglement resources that on average and these sets can always be discriminated locally with multiple copies of two-qubit maximally entangled states. These results also exhibit nontrivial signification of maximally entangled states in the local discrimination of quantum states.In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality in multipartite quantum systems. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving positive operator-valued measures on fixed subsystem and partially answer an open question given by Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. The connection between the nonlocality and the plane structure of OPSs is established. We successfully construct a strongly nonlocal OPS in ${\mathcal{C}}^{{d}_{A}}\ensuremath{\bigotimes}{\mathcal{C}}^{{d}_{B}}\ensuremath{\bigotimes}{\mathcal{C}}^{{d}_{C}}\phantom{\rule{4pt}{0ex}}({d}_{A},{d}_{B},{d}_{C}\ensuremath{\ge}4)$, which contains fewer quantum states, and generalize the structures of known OPSs to any possible three and four-partite systems. In addition, we propose several entanglement-assisted protocols for perfectly local discrimination of the sets. It is shown that the protocols without teleportation use less entanglement resources that on average and these sets can always be discriminated locally with multiple copies of two-qubit maximally entangled states. These results also exhibit nontrivial signification of maximally entangled states in the local discrimination of quantum states.

arXiv:2205.10813Physical Review ANov 15, 202214 citations

On a class of small nonlocal set of n-party orthogonal product states

Saronath Halder

It is shown that there exists a class of locally indistinguishable, completable, small set of $n$ -party ( $n\geq3$ ) orthogonal product states, with $2n(d-1)$ members in $(d)^{\otimes n}$ dimensions ( $d\geq2$ ), imposing the condition that no party is able to begin with a nontrivial and orthogonality preserving measurement in $d\times d$ dimensions. In fact, it is possible to construct a multipartite nonlocal orthogonal product basis in $(d)^{\otimes n}$ dimensions which contains fewer than $2n(d-1)$ such states (along with other product states) and that does not satisfy the above mentioned condition. As a result of which some information, useful for state discrimination, can be extracted without disturbing the orthogonality of the post measurement states. So, imposing such a condition, is related to the stronger form of nonlocality. Finally, it is shown that a $2\times2$ maximally entangled state as resource, along with a local protocol, is sufficient for perfect discrimination of such a nonlocal set of n-party orthogonal product states in $(d)^{\otimes n}$ dimensions.It is shown that there exists a class of locally indistinguishable, completable, small set of $n$-party ($n\geq3$) orthogonal product states, with $2n(d-1)$ members in $(d)^{\otimes n}$ dimensions ($d\geq2$), imposing the condition that no party is able to begin with a nontrivial and orthogonality preserving measurement in $d\times d$ dimensions. In fact, it is possible to construct a multipartite nonlocal orthogonal product basis in $(d)^{\otimes n}$ dimensions which contains fewer than $2n(d-1)$ such states (along with other product states) and that does not satisfy the above mentioned condition. As a result of which some information, useful for state discrimination, can be extracted without disturbing the orthogonality of the post measurement states. So, imposing such a condition, is related to the stronger form of nonlocality. Finally, it is shown that a $2\times2$ maximally entangled state as resource, along with a local protocol, is sufficient for perfect discrimination of such a nonlocal set of n-party orthogonal product states in $(d)^{\otimes n}$ dimensions.

Mar 28, 20162 citations

Maximally Entangled States of a Two-Qubit System

Manu Pratap Singh, B. S. Rajput

International Journal of Theoretical PhysicsAug 1, 201311 citations

It is shown that there exists a class of locally indistinguishable, completable, small set of

n

-party (

n\geq3

) orthogonal product states, with

2n(d-1)

members in

(d)^{\otimes n}

dimensions (

d\geq2

), imposing the condition that no party is able to begin with a nontrivial and orthogonality preserving measurement in

d\times d

dimensions. In fact, it is possible to construct a multipartite nonlocal orthogonal product basis in

(d)^{\otimes n}

dimensions which contains fewer than

2n(d-1)

such states (along with other product states) and that does not satisfy the above mentioned condition. As a result of which some information, useful for state discrimination, can be extracted without disturbing the orthogonality of the post measurement states. So, imposing such a condition, is related to the stronger form of nonlocality. Finally, it is shown that a

2\times2

maximally entangled state as resource, along with a local protocol, is sufficient for perfect discrimination of such a nonlocal set of n-party orthogonal product states in

(d)^{\otimes n}

dimensions.