Berry Groisman, Lev Vaidman
An alternative proof for existence of ``quantum nonlocality without entanglement'', i.e. existence of variables with product-state eigenstates which cannot be measured locally, is presented. A simple``nonlocal'' variable for the case of one-way communication is given and the limit for its approximate measurability is found.
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Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $|ψ\rangle$ require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on $|ψ\rangle$, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameter…
A thought experiment considering conservation of energy and momentum for a pair of free bodies together with their internal energy is used to show the existence of states that have localised position while being eigenstates of energy and momentum. These states are applicable to all varieties of physical bodies, including planets and stars in free motion in the universe. The states are compound entanglements of multiple free bodies in which the momenta of the bodies are anticorrelated so that they always sum to zero, while their total kinetic energy is anticorrelated with their internal energie…
For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is s…
Self-testing nonlocality without entanglement
本文提出了一种设备无关的自测试方法，证明仅使用非纠缠测量即可认证无纠缠非局域性，并实现真正的网络量子非局域性，从而建立了无纠缠非局域性与贝尔非局域性之间的联系。
Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty an infinite amount of entanglement must be distributed initially and all this entangleme…
Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. In contrast, when the system size is finite and the temperature is low enough, the system may not thermalize. In this case, the steady state is well described by the generalized Gibbs ensemble constructed by using highly nonlocal conserved quantities. We also show that this model exhibits pr…
A simple protocol for complete and deterministic Bell state measurement is proposed. It consists of measurements of nonlocal spin product operators with the help of shared entanglement as an ancillary resource. The protocol realizes not only nonlocal Bell state measurement between a pair of distant qubits but also a complete Bell filter that transmits either one of the Bell states indicated by the measurement outcome. These schemes will be useful in quantum technologies where nonlocal Bell state measurement is indispensable.
Nonlocal measurement, or instantaneous measurement of nonlocal observables, is a considerably difficult task even for a simple form of product observable since relativistic causality prohibits interaction between spacelike separate subsystems. Following a recent proposal for effectively creating the von Neumann measurement Hamiltonian of nonlocal observables [Brodutch and Cohen, Phys. Rev. Lett. 116, 070404 (2016)], here we report a proof-of-principle demonstration of nonlocally measuring a product observable using linear optics without the violation of relativistic causality. Our scheme provi…
It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.
Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum protocols owing to their good property. Thus a lot of attention are paid to how to construct a nonlocal set of orthogonal product states though it is a difficult problem. In this paper, we propose a novel general method to construct a nonlocal set of orthogonal product states in $\mathbb{C}^{d} \otimes \mathbb{C}^{d}$ for $d\geq3$. We give an ingenious proof for the local indistinguishability of those product states. The set of product states, which are constructed by our method, has a very good structure. Subsequentl…
The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence.
Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a shared maximally-entangled ancilla. We present a new approach to this problem, using the language of generalized quantum measurements, to show that it is actually possible to measure a nonlocal spin product observable without necessarily requiring a maximally-entangled ancilla. This approach opens the door to more economical arbitrary-strength nonlocal measuremen…
Nonlocality via multiqubit orthogonal product bases
本文研究多量子比特正交乘积基的局域可区分性，识别出无纠缠非定域基，并提出借助Bell态量子隐形传态合并系统的区分方案。
Recently, much attention have been paid to the constructions of nonlocal multipartite orthogonal product states. Among the existing results, some are relatively complex in structure while others have many constraint conditions. In this paper, we firstly give a simple method to construct a nonlocal set of orthogonal product states in $\otimes_{j=1}^{n}\mathbb{C}^{d}$ for $d\geq 2$. Then we give an ingenious proof for local indistinguishability of the set constructed by our method. According to the characteristics of this construction method, we get a new construction of nonlocal set with fewer …
Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. Concept of genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. Existence of such sets eventually motivates the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for arbitrary number of parties. Strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is po…
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems $\mathcal{C}^{d}\otimes\mathcal{C}^{d}\otimes\mathcal{C}^{d}~(d\geq3)$ and $\mathcal{C}^d\otimes \mathcal{C}^{d+1}\otimes \mathcal{C}^{d+2}~(d\geq 3)$. Then for general tripartite quantum system $\mathcal{C}^{n_{1}}\otimes\mathcal{C}^{n_{2}}\otimes\mathcal{C}^{n_{3}}$ $(3\leq n_{1}\leq n_{2}\leq n_{3})$, we obtain $2(n_{2}+n_{3}-1)-n_{1…
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in $d_A\otimes d_B\otimes d_C$ and $d_A\otim…
The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon o…
Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for …
It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality without entanglement. These nonlocal sets can be completable or uncompletable. In this work both completable and uncompletable small nonlocal sets of multipartite orthogonal product states are constructed. Apart from nonlocality, these sets have other interesting properties. In particular, the completable sets lead to the construction of a class of complete orthogonal product bas…
We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson model below the localization transition. We show that they display eigenstate thermalization for normalized observables. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of the…
Small set of orthogonal product states with nonlocality
本文研究小尺寸局部稳定正交乘积态集合，给出其尺寸下界，并揭示最小尺寸 UPB 的某些子集具有局部稳定性，从而体现更强的非定域性。
Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
针对多体系统中无纠缠强非定域正交集是否存在的问题，本文利用$N$维超立方体分解，为所有奇数$N\geq 3$构造强非定域正交集和不可扩展乘积基，并应用于量子秘密共享等场景。
An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties a…
Unextendible product operator basis
本文将非局域性概念从量子态扩展到算子，提出不可扩展乘积算子基及酉算子基等新概念，构造实例并证明其在LOCC下具有非局域性，且区分它们需要纠缠资源。
The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates
本文研究了费米子线性光学（FLO）广度的标度行为，证明了任意纯态与4量子比特宇称本征态张量积的FLO广度等于两因子广度之积，并递归证明了该广度对4量子比特魔态的任意张量积具有可乘性。
All product eigenstates in Heisenberg models from a graphical construction
本研究通过自旋超流基尔霍夫规则对含Dzyaloshinskii-Moriya相互作用的海森堡XXZ模型乘积本征态分类，统一了相关体系的大简并现象，构建了具广延简并度的自旋系统，为奇异凝聚态研究提供新方向。
Activation of quantum steering sharing with unsharp nonlocal product measurements
针对局域不锐测量难以支持非局域量子导引共享的问题，本文提出基于量子椭球构造最优不锐非局域乘积测量的方法，并证明其可在 GHZ 态中激活导引共享且无需复制态或损耗其他关联。
In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving POVM on fixed subsystem and partially answer an open question given by Yuan et al. Phys. Rev. A \textbf{102}, 042228 (2020)}. The connection between the nonlocality and the plane structure of OPS is established. We successfully construct a strongly nonlocal OPS in $\mathcal{C}^{d_{A}}\otimes \mathcal{C}^{d_{B}}\otimes \mathcal{C}^{d_{C}}$ $(d_{A,B,C}\geq 4)$, which contains few…
Strong quantum nonlocality without entanglement in every $(n-1)$-partition
本文在任意$n$体量子系统中构造了在每个$(n-1)$-划分中局部不可约的正交直积集合，证明其具有强非局域性且所需量子态更少，并回答了Zhang等人提出的开放问题。
We can only perform a finite rounds of measurements in protocols with local operations and classical communication (LOCC). In this paper, we propose a set of product states, which require infinite rounds of measurements in order to distinguish this given set of states perfectly by LOCC. Therefore, we can conclude that these sets of states are locally indistinguishable. More accurately, given any multipartite LOCC indistinguishable set where every local system cannot start with a nontrivial measurement, then after appending these states with arbitrarily choosing two nonorthogonal states, we obt…
Ensembles containing orthogonal product states are found to be indistinguishable under local operations and classical communication (LOCC), thereby showing irreversibility in the preparation and distinguishing processes, which is commonly known as nonlocality without entanglement. On the other hand, correlations arising from incompatible measurements on entangled states lead to Bell-nonlocality. We unify these two concepts from the change in certain property incurred in the ensemble under a suitable global unitary transformation. Specifically, we prove that under controlled-NOT (CNOT) operatio…
We point out two interesting features of position-momentum uncertainty product: $U=Δx Δp$. We show that two special (non-differentiable) eigenstates of the Schr{ö}dinger operator with the Dirac Delta potential $[V(x)=-V_0 δ(x)],V_0>0$, also satisfy the Heisenberg's uncertainty principle by yielding $U> \frac{\hbar}{2}$. One of these eigenstates is a zero-energy and zero-curvature bound state.
We present a generic method to construct a product basis exhibiting Nonlocality Without Entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of control-Discrete Fourier Transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct Unextendible Product Bases and their associated Bound Entangled States. To our knowledge, this is the first method which, given a general…
Practical Criteria for Entanglement and Nonlocality in Systems with Additive Observables
本文针对具有确定值可加可观测量的两体系统，推导了简单易用的纠缠与非定域性检测判据，给出了相关充要条件及CHSH不等式违反情形，并以LHC上希格斯到ZZ衰变的检测为例进行了验证。
Superactivation of Bell nonlocality in pure anyonic states
研究发现纯任何子态在集体测量下表现出非局域性的超激活现象，揭示了任何子态中纠缠与非局域性的关联。
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. In general, it is difficult to show that such an orthogonality-preserving local measurement must be trivial. In this work, we develop two basic techniques to deal with this problem. Using these techniques, we successfully show the existence of unexten…
We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of $\mathbb{C}^d\otimes\mathbb{C}^d$, where $d$ is odd, Zhang \emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {\bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system $\mathbb{C}^m\otimes\mathbb{C}^n$. We present a small …
We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the nondemolition property of the measurements have been performed with high precision showing the suitability of the scheme as a basic ingredient of numerous quantum information protocols. The method allows to demonstrate for the first time with strong measurements a special feature of pre- and postselected quantum systems: the failure of the product rule. It has been veri…
Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
本文推导了构建展现强量子非局域性的不可扩展可分基（UBB）的规则，解决了Agrawal等人提出的开放问题，为多体系统中真正纠缠子空间的信息论应用提供支持。
Nonlocality of tripartite orthogonal product states
针对多粒子系统中正交乘积态局域可区分性研究较少的问题，构造了三粒子系统中含18(d-1)个正交乘积态的局域不可区分子集并推广方法，还证明三量子比特GHZ态可作为资源区分这些态。
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an $n$-dimensional hypercube for $n= 3,4,5$, we successfully construct strongly nonlocal OPSs in any possible three, four and five-partite systems, which answers an open question given by Halder et al. [Phys. Rev. Lett.122, 040403 (2019)] and Yuan et al. [Phy…
Statistical link between Bell nonlocality and uncertainty relations
本文利用Aharonov-Vaidman恒等式建立Bell非定域性与不确定关系之间的统计联系，使Bell型不等式上界与多方量子系统的不确定关系上界相互关联。
Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit "quantum nonlocality without entanglement" if the states are locally indistinguishable, i.e. it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the no…
In this paper, we generalize the concept of strong quantum nonlocality from two aspects. Firstly in $\mathbb{C}^d\otimes\mathbb{C}^d\otimes\mathbb{C}^d$ quantum system, we present a construction of strongly nonlocal quantum states containing $6(d-1)^2$ orthogonal product states, which is one order of magnitude less than the number of basis states $d^3$. Secondly, we give the explicit form of strongly nonlocal orthogonal product basis in $\mathbb{C}^3\otimes \mathbb{C}^3\otimes \mathbb{C}^3\otimes \mathbb{C}^3$ quantum system, where four is the largest known number of subsystems in which there …
Total spin eigenstates can be used to intrinsically encode a direction, which can later be decoded by means of a quantum measurement. We study the optimal strategy that can be adopted if, as is likely in practical applications, only product states of $N$-spins are available. We obtain the asymptotic behaviour of the average fidelity which provides a proof that the optimal states must be entangled. We also give a prescription for constructing finite measurements for general encoding eigenstates.
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e. to share no prior randomness, this process can be simulated classically with bounded communication, using only 9 b…
Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
针对偶数 n 体系统中强非定域正交乘积集的存在性问题，本文给出一般构造，并利用纠缠资源提出更省纠缠的局域态区分协议及信息隐藏应用。
Efficient discrimination schemes for unextendible product bases with strong quantum nonlocality
本文提出三种高效区分具有强量子非局域性的不可扩展产物基的方案，利用最大化纠缠态减少资源消耗。
Coherently excited nonlocal quantum features using polarization-frequency correlation between quantum erasers
本文基于泊松分布相干光子对的偏振-频率关联，利用门控外差探测和滤波技术实现类空间分离量子擦除器间的非局域关联，并数值验证了贝尔不等式违背。
Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States
本文提出DMRG-S矩阵乘积态算法，在80格点Rydberg阻塞链中提取疤痕本征态，并发现新的精确MPS疤痕态。
The inverse problem of 'eigenstates-to-Hamiltonian' is considered for an open chain of $N$ quantum spins in the context of Many-Body-Localization. We first construct the simplest basis of the Hilbert space made of $2^N$ orthonormal Matrix-Product-States (MPS), that will thus automatically satisfy the entanglement area-law. We then analyze the corresponding $N$ Local Integrals of Motions (LIOMs) that can be considered as the local building blocks of these $2^N$ MPS, in order to construct the parent Hamiltonians that have these $2^N$ MPS as eigenstates. Finally we study the Matrix-Product-Operat…
In this paper we investigate the nonlocal correlation (beyond entanglement) captured by measurement induced nonlocality and geometric quantum discord for a pair of interacting spin-1/2 particles at thermal equilibrium. It is shown that both the measures are identical in measuring the correlation. We show the possibility of nonlocal correlation between the spins without entanglement, which ceases to exist only for the maximal mixture of product bases. We also observe that while interaction between the spins is responsible for the enhancement of correlation, this non-classicality decreases with …
Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the local indistinguishability of a set of orthogonal product states. In this paper we analyze the character of operators to distinguish a set of full product bases in a multi-partite system, and show that distinguishing perfectly a set of full product bases needs only local projective measurements and classical communication, and these measurements cannot damage each product basis. Employing these conclusions one can discuss local distinguishability of full product bases ea…
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。
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。
We reexamine quantum correlation from the fundamental perspective of its consanguineous quantum property, the coherence. We emphasize the importance of specifying the tensor product structure of the total state space before discussing quantum correlation. A measure of quantum correlation for arbitrary dimension bipartite states using nonlocal coherence is proposed, and it can be easily generalized to the multipartite case. The quantification of non-entangled component within quantum correlation is investigated for certain states.
Local dynamics and the structure of chaotic eigenstates
本研究以(1+1)维自旋链为例，揭示局域相互作用混沌系统本征态的新普适性质，阐明系数幅值的普适形式、幺正性与局域性带来的关联及其对热化过程相关物理量的影响。
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。
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