One-way Local Operations And Classical Communication Research Articles

Chordal graphs and distinguishability of quantum product states

We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the key graph structure that drives distinguishability in one-way LOCC, and we derive a one-way LOCC characterization for chordal graphs that establishes a connection with the theory of matrix completions. We also derive minimality conditions on graph parameters that allow for the determination of indistinguishability of states. We present a number of applications and examples built on these results.

Local discrimination of lattice states via complete graph

In this paper, we use graph theory to study the distinguishability of lattice states under local operations and classical communication (LOCC) in . Firstly, we present that for the basis of lattice unitary matrices, there are (p 2 + 1)(p + 1) distinct maximal commuting sets in p 2-dimensional system. Secondly, for any set of lattice states, we can obtain a graph G which consists of some k-complete subgraphs. Using the graph G, we show that the set can be distinguished by one-way LOCC if , where n is the number of vertices of a graph G and s k is the number of k-complete subgraphs. Moreover, we also proved that this conclusion is necessary and sufficient in . For system, our result can cover the results in (2015, Phys. Rev. A 92, 042 320); (2020, Sci. China-Phys. Mech. Astron. 63, 280 312).

Distinguishability of generalized Bell states in arbitrary dimension system via one-way local operations and classical communication

We investigate the distinguishability of generalized Bell states (GBSs) in arbitrary dimension system by one-way local operations and classical communication (LOCC). Firstly, by analyzing three local unitary transformations, we define two concepts for each set $$\mathcal {L}$$ of GBSs, i.e., an admissible solutions set $$\mathcal {S}_{\mathcal {A}}$$ and a genuinely nonadmissible solutions set $$\mathcal {S}_{\mathcal {L}}$$ . Then, we show that a set $${\mathcal {L}}$$ of any GBSs can be distinguished by one-way LOCC if $${\mathcal {S}}_{\mathcal {A}}\backslash {\mathcal {S}}_{\mathcal {L}}$$ is nonempty. Fan’s and Wang et al.’s results (Phys Rev Lett 92:177905, 2004: Phys Rev A 99:022307, 2019) can be covered by our result. Comparing with Wang et al.’s result, our successful ratio of local distinguishability improves markedly, especially for even dimension system. In some cases, it can increase by nearly $$42\%$$ . However, there are still some cases where our method cannot work. For the uncovered cases, we define an uncovered set and present that there is no method which is more powerful than ours for local discrimination of GBSs if the uncovered set is a subset of the different set of GBSs.

Local distinguishability of generalized Bell states with one ebit of entanglement

It is an interesting topic how much entanglement resources are necessary to distinguish locally indistinguishable orthogonal quantum states by local operations and classical communication (LOCC). Using only one ebit of entanglement some locally indistinguishable orthogonal product bases can be distinguished by LOCC [2019 Phys. Rev. A 99 012343]. However, it is still an open question whether one ebit of entanglement is sufficient for distinguishing a locally indistinguishable set of orthogonal maximally entangled states. We focus on the generalized Bell states (GBSs), and firstly find that any four GBSs in a 4 ⊗ 4 quantum system are always distinguished by one-way LOCC using one ebit of entanglement. Then we consider a general case, i.e., d ⊗ d quantum system (d is even), and show that the set of any GBSs can be distinguished by one-way LOCC using one ebit of entanglement if is nonempty, where is the admissible solutions set of and is the genuinely nonadmissible solutions set of . This criterion is very simple and convenient since only some congruence equations are calculated. Finally, we find a curious and counterintuitive case, i.e., in a 3 ⊗ 3 quantum system there exist four GBSs which cannot be distinguished by one-way LOCC using one ebit of entanglement, although the dimension of the subsystem is less than four. These results can help us better understand the role of entanglement as a resource in local state discrimination problems.

One-way LOCC indistinguishable lattice states via operator structures

Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory that are built on the structure theory of operator systems and operator algebras, to develop a technique for the construction of relatively small sets of lattice states not distinguishable by one-way LOCC schemes. We also present examples, show the construction extends to generalized Pauli states, and compare the construction to other recent work.

A Note on the Relationship Between Genuinely Coherence and Generalized Entanglement Monotones

We find a one to one mapping between genuinely incoherent operations and special one-way local operations and classical communication(LOCC) for density matrices with full rank. We also define “generalized entanglement monotones” and “genuinely coherence monotones” under special one-way LOCC and genuinely incoherent operations respectively. Any entanglement monotone proposed by Vidal et al. is a generalized entanglement monotone. Any coherence monotone under incoherent operations is a genuinely coherence monotone. Furthermore, we clarify the relationship between generalized entanglement monotones and genuinely coherence monotones. We demonstrate that any generalized entanglement monotone of bipartite pure state is the lower bound of a suitable genuinely coherence monotone; any genuinely coherence monotone of a quantum state is the generalized entanglement monotone of the corresponding maximally correlated state.

One-shot entanglement distillation beyond local operations and classical communication

We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows for a straightforward comparison of their exact achievable performance, we relate the fidelity of distillation under these classes of operations with a family of entanglement monotones and the rates of distillation with a class of smoothed entropic quantities based on the hypothesis testing relative entropy. We then characterise exactly the one-shot distillable entanglement of several classes of quantum states and reveal many simplifications in their manipulation. We show in particular that the ε-error one-shot distillable entanglement of any pure state is the same under all sets of operations ranging from one-way LOCC to separability-preserving operations or operations preserving the set of states with positive partial transpose, and can be computed exactly as a quadratically constrained linear program. We establish similar operational equivalences in the distillation of isotropic and maximally correlated states, reducing the computation of the relevant quantities to linear or semidefinite programs. We also show that all considered sets of operations achieve the same performance in environment-assisted entanglement distillation from any state.

Quantum error correction and one-way LOCC state distinguishability

We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction properties, emphasizing an operator theory approach to the subject, and we obtain new applications to one-way LOCC state distinguishability as well as new derivations of some established results. We also derive conditions on when states that arise through the stabilizer formalism for quantum error correction are distinguishable under one-way LOCC.

One-way local distinguishability of generalized Bell states in arbitrary dimension

In this paper, we study the distinguishability of arbitrary dimensional generalized Bell states under one-way local operations and classical communication (LOCC). We introduce an admissible solutions set and a nonadmissible solutions set for each set of generalized Bell states. Any element that exists in the admissible solution set but not in the nonadmissible one implies the one-way LOCC distinguishablity of a given set. This criterion is very convenient in the following two aspects: both solution sets can be calculated easily and, once the criterion can be applied successfully for a given set, it immediately presents an explicit distinguishing strategy. Furthermore, Fan's results in Phys. Rev. Lett. 92, 177905 (2004) can also be deduced as special cases of our results. For the case no such element exists, we disprove a conjecture proposed by Yang et al. in Quantum Inf. Process. 17, 29 (2018) by presenting a counterexample.

Locally indistinguishable generalized Bell states with one-way local operations and classical communication

In this paper, we investigate the indistinguishability of generalized Bell states (GBSs) by one-way local operations and classical communication (LOCC). We first introduce two sets, i.e., the difference set and the testing set, and show that the GBSs cannot always be distinguished by one-way LOCC if the testing set is a subset of the difference set of GBSs. Then we give a unified upper bound about indistinguishable GBSs by one-way LOCC. The newly derived bound is smaller than those presented in Zhang et al. [Phys. Rev. A 91, 012329 (2015)] and Wang et al. [Quantum Inf. Process. 15, 1661 (2016).]. More precisely, the minimum number of one-way locally indistinguishable GBSs is not more than $2\ensuremath{\lceil}\sqrt{d}\ensuremath{\rceil}+\ensuremath{\lceil}\frac{\sqrt{d}}{4}\ensuremath{\rceil}+1$.

Local distinguishability of generalized Bell states

We investigate the distinguishability of orthogonal generalized Bell states (GBSs) in $$d\otimes d$$ system by local operations and classical communication (LOCC), where d is a prime. We show that |S| is no more than $$d+1$$ for any l GBSs, i.e., $$|S|\le d+1$$ , where S is maximal set which is composed of pairwise noncommuting pairs in $${\varDelta } U$$ . If $$|S|\le d$$ , then the l GBSs can be distinguished by LOCC according to our main Theorem. Compared with the results (Fan in Phys Rev Lett 92:177905, 2004; Tian et al. in Phys Rev A 92:042320, 2015), our result is more general. It can determine local distinguishability of $$l (> k)$$ GBSs, where k is the number of GBSs in Fan’s and Tian’s results. Only for $$|S|=d+1$$ , we do not find the answer. We conjecture that any l GBSs cannot be distinguished by one-way LOCC if $$|S|=d+1$$ . If this conjecture is right, the problem about distinguishability of GBSs with one-way LOCC is completely solved in $$d\otimes d$$ .

On small set of one-way LOCC indistinguishability of maximally entangled states

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.

Local distinguishability of maximally entangled states in canonical form

In this paper, we mainly study the local distinguishability of mutually orthogonal maximally entangled states in canonical form. In $$d \otimes d$$d?d, Nathanson (Phys Rev A 88:062316, 2013) presented a feasible necessary and sufficient condition for distinguishing the general bipartite quantum states by one-way local operations and classical communication (LOCC). However, for maximally entangled states in canonical form, it is still unknown how to more effectively judge whether there exists a state such that those unitary operators corresponding to those maximally entangled states are pairwise orthogonal. In this work, we exhibit one method which can be used to more effectively judge it. Furthermore, we construct some sets of maximally entangled states and can easily know that those states are not distinguished by one-way LOCC with the help of our new method.

Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements.

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandão and Harrow's de Finetti theorem where a kind of partially-one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i)a quasipolynomial-time algorithm which detects multipartite entanglement with an amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii)a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.

Distinguishing maximally entangled states by one-way local operations and classical communication

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.

Composability of partial-entanglement-breaking channels via entanglement-assisted local operations and classical communication

We consider composability of quantum channels from a limited amount of entanglement via local operations and classical communication (LOCC). We show that any $k$-partially entanglement breaking channel can be composed from an entangled state with Schmidt number of $k$ via one-way LOCC. From the entanglement assisted construction we can reach an alternative definition of partially entanglement breaking channels.

Three maximally entangled states can require two-way local operations and classical communication for local discrimination

We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$-dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.

One-way LOCC indistinguishability of maximally entangled states

In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of $$d-1$$d-1 indistinguishable maximally entangled states by one-way LOCC are demonstrated in $$d \otimes d$$d?d (for $$d=7, 8, 9, 10$$d=7,8,9,10). Interestingly, we discover there exist sets of $$d-2$$d-2 such states in $$d \otimes d$$d?d (for $$d=8, 9, 10$$d=8,9,10), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist $$d-1$$d-1 or fewer indistinguishable maximally entangled states in $$d \otimes d(d \ge 5)$$d?d(d?5) by one-way LOCC.

LOCC distinguishability of unilaterally transformable quantum states

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.

On the existence of LOCC-distinguishable bases in three-dimensional subspaces of bipartite 3 × n systems

We present numerical evidence showing that any three-dimensional subspace of has an orthonormal basis which can be reliably distinguished using one-way LOCC (local operations and classical communication), where a measurement is made first on the three-dimensional part and the result used to select an optimal measurement on the n-dimensional part. We also show that the order of measurement is essential, by providing an example of a three-dimensional subspace of which does not have any basis that can be distinguished by measuring first on the five-dimensional factor.