John Watrous
It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment.
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We give a simple proof, based on time-reversibility and purity, that a complete orthonormal family of pure states which can be perfectly distinguished by LOCC cannot contain any entangled state. Our results are really about the shape of certain states and processes, and are valid in arbitrary categorical probabilistic theories with time-reversal. From the point of view of the resource theory of entanglement, our results can be interpreted to say that free processes can distinguish between the states in a complete orthonormal family only when the states themselves are all free.
In this paper, we construct $2n-1$ locally indistinguishable orthogonal product states in $\mathbb{C}^n\otimes\mathbb{C}^{4}~(n>4)$ and $\mathbb{C}^n\otimes\mathbb{C}^{5}~(n\geq 5)$ respectively. Moreover, a set of locally indistinguishable orthogonal product states with $2(n+2l)-8$ elements in $\mathbb{C}^n\otimes\mathbb{C}^{2l}~(n\geq 2l>4)$ and a class of locally indistinguishable orthogonal product states with $2(n+2k+1)-7$ elements in $\mathbb{C}^n\otimes\mathbb{C}^{2k+1}~(n\geq 2k+1>5)$ are also constructed respectively. These classes of quantum states are then shown to be distinguishabl…
We provide a unifying framework for exact, probabilistic, and approximate conversions by local operations and classical communication (LOCC) between bipartite states. This framework allows us to formulate necessary and sufficient conditions for LOCC conversions from pure states to mixed states and it provides necessary conditions for LOCC conversions between mixed states. The central idea is the introduction of convex sets for exact, probabilistic, and approximate conversions, which are closed under LOCC operations and which are largely characterized by simple properties of pure states.
Classifying locally distinguishable sets: No activation across bipartitions
本文通过引入等级体系，对局部可区分集进行分类，探讨了在多粒子系统中通过OP-LOCC转换的可能性及“跨双分区无激活”现象。
In this article, we show a sufficient and necessary condition for locally distinguishable bipartite states via one-way local operations and classical communication (LOCC). With this condition, we present some minimal structures of one-way LOCC indistinguishable quantum state sets. As long as an indistinguishable subset exists in a state set, the set is not distinguishable. We also list several distinguishable sets as instances.
The problem behind this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of $k=1$, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfe…
In this paper, we treat a local discrimination problem in the framework of asymmetric hypothesis testing. We choose a known bipartite pure state $\ketΨ$ as an alternative hypothesis, and the completely mixed state as a null hypothesis. As a result, we analytically derive an optimal type 2 error and an optimal POVM for one-way LOCC POVM and Separable POVM. For two-way LOCC POVM, we study a family of simple three-step LOCC protocols, and show that the best protocol in this family has strictly better performance than any one-way LOCC protocol in all the cases where there may exist difference betw…
In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and separable POVMs. As a result, we derive single-letterized formulas for the Stein's lemma type of optimal error exponents under one-way LOCC, two-way LOCC and separable POVMs, the Chernoff bounds under one-way LOCC POVMs and separable POVMs, and the Hoeffding bounds under one-way LOCC POVMs in the whole region of a parameter and under separable POVMs on a restricted…
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to dis…
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 …
Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state
本文研究纯双体态与完全混合态在单向、双向 LOCC 及可分 POVM 下的非对称渐近态辨识，给出 Hoeffding 界与三阶 Stein 型误差指数，并揭示两轮通信可达到可分操作最优性能而单向 LOCC 不能。
In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyze orthogonal product states in any system to show that with LOCC protocols, to distinguish seven orthogonal product states, one can exclude four states via a single copy. In bipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $\left \lceil \frac{N}{4} \right \rceil$ copies are allowed, where $\left \lceil l\right \rceil$ for a real number $l$ means the smallest integer not less than $l$. In multipartite systems, this result implies that N orthogo…
Incompleteness is necessary for activation of nonlocality without entanglement
本文证明任何初始局域可区分的完备正交积基在保正交局域投影测量下保持可区分，从而排除通过此类测量激活非局域性，并引入“强局域集”概念刻画LOCC可区分性的不可逆损失边界。
Distinguishability is a fundamental and operational task generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and also characterises capabilities of related information tasks. In this work, we consider discrimination between bipartite two-qubit unitary transformations by local operations and classical communication (LOCC) and its relations to entangling capabilities of given unitaries. We show that a pair of entangling unitaries which do not contain local parts, if they…
Given n-copies of unknown bipartite (possiblly mixed) state, our task is to test whether the state is a pure state of not. Allowed to use the global operations, optimal one-sided error test is the projection onto the symmetric subspace, obviously. Is it possible to approximate the globally optimal measurement by LOCC when n is large?
In this paper, we mainly study the local distinguishable multipartite quantum states by local operations and classical communication (LOCC) in $m_1\otimes m_2\otimes\ldots\otimes m_n$ , where the quantum system $m_1$ belongs to Alice, $m_2$ belongs to Bob, \ldots and $m_n$ belongs to Susan. We first present the pure tripartite distinguishable orthogonal quantum states by LOCC in $m_1\otimes m_2\otimes m_3$. With the conclusion in $m_1\otimes m_2\otimes m_3$, we prove distinguishability or indistinguishability of some quantum states. At last, we give the $n$-party distinguishable quantum states…
Unambiguous state discrimination of two mixed bipartite states via local operations and classical communications (LOCC) is studied and compared with the result of a scheme realized via global measurement. We show that the success probability of a global scheme for mixed-state discrimination can be achieved perfectly by the local scheme. In addition, we simulate this discrimination via a pair of pure entangled bipartite states. This simulation is perfect for local rather than global schemes due to the existence of entanglement and global coherence in the pure states. We also prove that LOCC pro…
We show that an arbitrary basis of a multipartite quantum state space consisting of $K$ distant parties such that the $k$th party has local dimension $d_k$ always contains at least $N=\sum_{k=1}^K (d_k-1)+1$ members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show this lower bound is optimal by analytically constructing a special product basis having only $N$ members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon ``nonlocality without entan…
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$_{1}$, PPT and SEP distinguishabilities. We…
We investigate the asymptotic rates of entanglement transformations for bipartite mixed states by local operations and classical communication (LOCC). We analyse the relations between the rates for different transitions and obtain simple lower and upper bound for these transitions. In a transition from one mixed state to another and back, the amount of irreversibility can be different for different target states. Thus in a natural way, we get the concept of "amount" of irreversibility in asymptotic manipulations of entanglement. We investigate the behaviour of these transformation rates for di…
The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication
本研究证明三能级-高维系统中所有三维子空间在单向LOCC下存在可区分基，解决开放问题，并给出容量下界及状态转换应用。
A subspace of a multipartite Hilbert space is called \textit{locally indistinguishable} if any orthogonal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any $m\otimes n$ bipartite system such that $m>2$ and $n>2$ has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem. We settle this problem by showing that any $2\otimes n$ bipartite subspace is locally distinguishable in the sense it con…
Two types of results are presented for distinguishing pure bipartite quantum states using Local Operations and Classical Communications. We examine sets of states that can be perfectly distinguished, in particular showing that any three orthogonal maximally entangled states in C^3 tensor C^3 form such a set. In cases where orthogonal states cannot be distinguished, we obtain upper bounds for the probability of error using LOCC taken over all sets of k orthogonal states in C^n tensor C^m. In the process of proving these bounds, we identify some sets of orthogonal states for which perfect distin…
Any deterministic bipartite entanglement transformation involving finite copies of pure states and carried out using local operations and classical communication (LOCC) results in a net loss of entanglement. We show that for almost all such transformations, partial recovery of lost entanglement is achievable by using $2 \times 2$ auxiliary entangled states, no matter how large the dimensions of the parent states are. For the rest of the special cases of deterministic LOCC transformations, we show that the dimension of the auxiliary entangled state depends on the presence of equalities in the m…
We consider a realistic setting of quantum tasks that generate shared bipartite quantum states. Suppose \alice and \bob are located at different places and need to produce a target shared quantum state $ρ$. In order to save quantum communication, they can choose to share a proper smaller quantum state $σ$ first, and then turn $σ$ to $ρ$ by performing only local quantum operations and classical communications (LOCC). We hope $σ$ is the optimal such that the quantum communication needed is as little as possible, which is called the generation cost of $ρ$. In this paper, for an arbitrary bipartit…
Graph Structures for Local Distinguishability of Quantum Product States
利用图论研究量子乘积态在有限步双向LOCC下的局域可区分性，推导可区分图集的闭包性质并分类保证可区分性的图类。
We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily in tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglem…
Now, the known ensembles of orthogonal states which are distinguishable by local operators and classical communication (LOCC) satisfy the condition that the sum of Schmidit numbers of the orthogonal states is not bigger than the dimensions of the whole space. A natural question is whether an arbitary ensembles of LOCC-distinguishable orthogonal states satisfies the condition. We first show that, in this paper, the answer is positive. Then we generalize it into multipartite systems, and show that a necessary condition for LOCC-distinguishability of multipartite orthogonal quantum states is that…
A novel criterion of extracting thermodynamical work from a bipartite pure qudit-entangled state by means of local operation and classical communication (LOCC) has been presented. We have shown that non-vanishing $G$-concurrence is a necessary condition to extract work from an higher dimensional entangled state in LOCC paradigm.
In the general bipartite quantum system $m \otimes n$, Wang \emph{et al.} [Y.-L Wang \emph{et al.}, Phys. Rev. A \textbf{92}, 032313 (2015)] presented $3(m+n)-9$ orthogonal product states which cannot be distinguished by local operations and classical communication (LOCC). In this paper, we aim to construct less locally indistinguishable orthogonal product states in $m\otimes n $. First, in $3\otimes n (3< n)$ quantum system, we construct $3n-2$ locally indistinguishable orthogonal product states which are not unextendible product bases. Then, for $m\otimes n (4\leq m\leq n)$, we present $3n+m…
An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an Unentangled Orthogonal Basis (UOB). In general, for $n$ qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of $2^n-1$ two-spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally …
Entanglement is a resource to overcome the natural restriction of operations used for state manipulation to Local Operations assisted by Classical Communication (LOCC). Hence, a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via LOCC. In the multipartite setting no such state exists. There, rather a whole set, the Maximally Entangled Set of states (MES), which we recently introduced, is required. This set has on the one hand the property that any state outside of this set can be obtained via LOCC from one of the states within the …
Nonlocality without entanglement for multipartite quantum measurements
本研究证明两量子比特乘积测量在联合访问时可区分但局部分布时不可区分，建立无纠缠非局域性的测量类比，并揭示自适应协议优势、方向性及构造n-qubit测量对，最后展示光学实现。
We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical communication. The corresponding minimal quantum coherence is the entanglement of formation. Connections to the relative entropy of entanglement and quantum coherence, and generalizations to the multiparty case are also considered.
We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \leq d$ orthogonal maximally entangled states in $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ that are not perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys. Rev. Lett. 109 020506 (2012) -- arXiv:1107.3224 [quant-ph]] gives an affirmative answer for the case $k = d$. We give, for the first time, a proof that such sets of states indeed exist even in the case $k < d$. Our result is constructive …
Nonlocality without entanglement in exclusion of quantum states
本文研究了量子态排除任务，揭示了非纠缠情况下的非局域性现象，证明了三个双体产品态可全局抗区分但无法LOCC抗区分。
Quantum nonlocality without entanglement and state discrimination measures
研究无纠缠的量子非定域性与态判别度量的关系，给出由六个线性独立、等概率积态组成的集合，表明LOCC对其无法实现最优最小错误判别，但可实现最优无歧义判别。
Local distinguishability of six bipartite orthogonal product states
研究六个二分正交乘积态在任意二分量子系统上的局域可区分性，通过成对正交关系向量分类为八类共78种情况，其中73种可通过LOCC完美区分，并详细讨论剩余五种情况。
Extending Schmidt vector from pure to mixed states for characterizing entanglement
本研究利用优超格结构将Schmidt向量从纯态扩展至混合两体态，证明其在LOCC下具有单调性且能表征可分与最大纠缠态，并据此引入了一族纠缠单调量。
Pure state entanglement and von Neumann algebras
本文研究了由可交换冯·诺依曼代数表示的双部分量子系统中LOCC操作的理论，扩展了尼尔森定理，并揭示了不同类型因子与纠缠属性之间的对应关系。
Local distinguishability of five orthogonal product states on bipartite and tripartite quantum systems
本文研究五组正交产品态在双亲和三亲量子系统中的局部可区分性，通过定义正交关系向量分类并证明部分类别可被LOCC完美区分，推动了量子非局域性研究。
Entanglement cost of bipartite quantum channel discrimination under positive partial transpose operations
本研究提出双分量量子通道鉴别的纠缠成本理论，通过k-可注入PPT测试器分析最优成功概率，并利用SDP方法计算纠缠成本。
An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the subspace complementary to any UPB is a bound entangled state. We exhibit a tripartite 2x2x2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e. all three corresponding 2x4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local POVMs and classical commun…
The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. The relevant figure of merit is the maximal ratio (called data hiding ratio) between the distinguishability norms associated with the two sets of measurements we are comparing, typically all measurements vs LOCC protocols. For a bipartite $n\times n$ quantum system, it is known that the data hiding ratio scales as $n$, i.e. the square root of the re…
Maximally entangled mixed states for a fixed spectrum do not always exist
本文研究了固定谱混合态集合中是否存在极大纠缠态，通过分析秩为2状态，证明在特定特征值下不存在能在LOCC或非纠缠操作下转换为所有等谱状态的极大纠缠态。
Unextendible entanglement of quantum channels
本文利用超信道框架和$k$-可扩展性，定义了在单向LOCC超信道下单调递减的“信道不可扩展纠缠”度量，为资源提纯和零误差通信量提供上界，并提出半正定程序进行计算评估。
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