In the topic of distinguishment of orthogonal states in dd bipartite system,with the way of judging dimension of there corresponding orthogonal complement,and then determine whether the orthogonal complement space contains a maximally Abelian subspace,at last propose a new algorithm to distinguish states based on one-way LOCC.For generalized orthogonal Bell states in 44 bipartite system,by studying their distinguishment,this paper propose a faster algorithm based on one way LOCC.Experimental results show that the algorithm in ddbipartite system can be applies in distinguishing any orthogonal bipartite states.What’s more,the algorithm in 44 bipartite system is less complicated.
In the topic of perfect local distinguishability of orthogonal multipartite quantum states, most results obtained so far pertain to bipartite systems whose subsystems are of specific dimensions. In contrast very few results for bipartite systems whose subsystems are of arbitrary dimensions, are known. This is because a rich variety of (algebraic or geometric) structure is exhibited by different sets of orthogonal states owing to which it is difficult to associate some common property underlying them all, i.e., a common property that would play a crucial role in the local distinguishability of these states. In this Rapid Communication, I propose a framework for the distinguishability by one-way local operations and classical communication (1-LOCC) of sets of orthogonal bipartite states in a ${d}_{A}\ensuremath{\bigotimes}{d}_{B}$ bipartite system, where
dA,dB are the dimensions of both subsytems, labeled as
A and
B. I show that if the
ith party (where
i=A,B) can initiate a 1-LOCC protocol to perfectly distinguish among a set of orthogonal bipartite states, then the information of the existence of such a 1-LOCC protocol lies in a subspace of ${d}_{i}\ifmmode\times\else\texttimes\fi{}{d}_{i}$ Hermitian matrices, denoted by ${\mathcal{T}}_{\ensuremath{\perp}}^{(i)}$, and that the method to extract this information (of the existence of this 1-LOCC protocol) from ${\mathcal{T}}_{\ensuremath{\perp}}^{(i)}$ depends on the value of $\mathrm{dim}{\mathcal{T}}_{\ensuremath{\perp}}^{(i)}$. In this way one can give sweeping results for the 1-LOCC (in)distinguishability of all sets of orthogonal bipartite states corresponding to certain values of $\mathrm{dim}{\mathcal{T}}_{\ensuremath{\perp}}^{(i)}$. Thus I propose that the value of $\mathrm{dim}{\mathcal{T}}_{\ensuremath{\perp}}^{(i)}$ gives the common underlying property based on which sweeping results for the 1-LOCC (in)distinguishability of orthogonal bipartite quantum states can be made.
In the topic of perfect local distinguishability of orthogonal multipartite quantum states, most results obtained so far pertain to bipartite systems whose subsystems are of specific dimensions. In contrast very few results for bipartite systems whose subsystems are of arbitrary dimensions, are known. This is because a rich variety of (algebraic or geometric) structure is exhibited by different sets of orthogonal states owing to which it is difficult to associate some common property underlying them all, i.e., a common property that would play a crucial role in the local distinguishability of these states. In this paper, I propose a framework for the distinguishability by one-way LOCC (
1-LOCC) of sets of orthogonal bipartite states in a
dA⊗dB bipartite system, where
dA,dB are the dimensions of both subsytems, labelled as
A and
B. I show that if the
i-th party (where
i=A,B) can initiate a
1-LOCC protocol to perfectly distinguish among a set of orthogonal bipartite states, then the information of the existence of such a
1-LOCC protocol lies in a subspace of
di×di hermitian matrices, denoted by $\Tb^{(i)}$, and that the method to extract this information (of the existence of this
1-LOCC protocol) from $\Tb^{(i)}$ depends on the value of $dim \Tb^{(i)}$. In this way one can give sweeping results for the
1-LOCC (in)distinguishability of all sets of orthogonal bipartite states corresponding to certain values of $dim \Tb^{(i)}$. Thus I propose that the value of $dim \Tb^{(i)}$ gives the common underlying property based on which sweeping results for the
1-LOCC (in)distinguishability of orthogonal bipartite quantum states can be made.
In this paper, we mainly study the local indistinguishability of mutually orthogonal bipartite maximally entangled states. We construct sets of fewer than
d orthogonal maximally entangled states which are not distinguished by one-way local operations and classical communication (LOCC) in the Hilbert space of $d\ensuremath{\bigotimes}d$. The proof, based on the Fourier transform of an additive group, is very simple but quite effective. Simultaneously, our results give a general unified upper bound for the minimum number of one-way LOCC indistinguishable maximally entangled states. This improves previous results which only showed sets of $N\ensuremath{\ge}d\ensuremath{-}2$ such states. Finally, our results also show that previous conjectures in Zhang et al. [Z.-C. Zhang, Q.-Y. Wen, F. Gao, G.-J. Tian, and T.-Q. Cao, Quant. Info. Proc. 13, 795 (2014)] are indeed correct.
We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way local operations and classical communication (LOCC) where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N ⩽ d maximally entangled states in d ⊗ d for d = 4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly, for d = 5,6, our examples consist of four and five states, respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.
It is necessary to investigate the local distinguishability of orthogonal quantum state sets, as their adoption in protocol design helps diminish quantum state transmission and cut operational costs. In this paper, we explore the local distinguishability of six orthogonal product states (OPSs) on any bipartite quantum system. We classify different sets of six bipartite OPSs into eight categories by using the vectors of the numbers of pairwise orthogonality relations, where any two states are orthogonal on only one subsystem within each set. We find that these eight categories contain a total of 78 distinct cases, all but five of which are perfectly distinguishable via local operations and classical communication (LOCC). Furthermore, we discuss the local distinguishability of those five distinct cases in detail. Our work explicitly characterizes the local distinguishability of six bipartite OPSs.