Daegene Song
Several proposed quantum computer models include measurement processes, in order to implement nonlocal gates and create necessary entanglement resources during the computation. We introduce a scheme in which the measurements can be delayed for two- and three-qubit nonlocal gates. We also discuss implementing arbitrary nonlocal gates when measurements are included during the process.
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Nonlocal gate operation is based on sharing an ancillary pair of qubits in perfect entanglement. When the ancillary pair are partially entangled, the efficiency of the gate operation drops. Using general transformations, we devise probabilistic nonlocal gates, which perform the nonlocal operation conclusively when the ancillary pair are only partially entangled. We show that a controlled purification protocol can be implemented by the probabilistic nonlocal operation.
Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron a…
We propose an experimentally feasible scheme to realize the nonlocal gate between two different quantum network nodes. With an entanglement-qubit (ebit) acts as a quantum channel, our scheme is resistive to actual environment noise and can get high fidelity in current cavity quantum electrodynamics (C-QED) system.
On the Experimental Determination of Nonlocal Characteristics of Two-Qubit Gates
本文基于su(4)卡当子代数元素生成的两比特门的纠缠能力和门典型性表达式，构建量子电路来测量两比特门的这两种特性以确定其非局域特性，通过调整CNOT门数量减少测量纠缠能力的电路数量，且测量门典型性需更多非局域资源。
It is known from Schmidt decomposition that Schmidt number of nonlocal two-qubit quantum gates is 2 or 4. We identify conditions on geometrical points of a gate to have Schmidt number 2. A simple analysis reveals that Schmidt number 2 corresponds to controlled unitary gates with CNOT being the only perfect entangler. Further, it is shown that Schmidt strength and entangling power are maximum only for CNOT in the controlled unitary family.
We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic gates, is investigated. Additionally, the influence of quantum decoherence on holonomic teleportation used as a computational primitive is studied. Advantages of the holonomic implementation with respect to control errors and dissipation are presented.
We experimentally demonstrate, with an all-optical setup, a nonlocal deterministic quantum non-demolition interaction gate applicable to quantum states at nodes separated by a physical distance and connected by classical communication channels. The gate implementation, based on entangled states shared in advance, local operations, and classical communication, runs completely in parallel fashion at both the local nodes, requiring minimum resource. The nondemolition character of the gate up to the local unitary squeezing is verified by the analysis using several coherent states. A genuine quantu…
Nonlocal characteristics and argand diagram of two-qubit gates
研究两量子比特门的非局域特性，通过分析其非局域部分的平方本征值和弦长，揭示纠缠能力与门典型性的表达方式，并划分完美纠缠器的区域。
Optimal Two-Qubit Gate-Cutting Cost and Measures of Nonlocality
本研究从最优双量子比特门切割公式出发，推导出拟概率范围与五个非局域性描述符的尖锐上下界，揭示门切割成本在相似非局域门间的显著差异。
Heralded nonlocal quantum gates for distributed quantum computation in a decoherence-free subspace
本文提出一种可预告的非局域量子门协议，通过动态控制演化并借助辅助原子后选择，在退相干自由子空间内实现高保真分布式量子计算。
We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and are deterministic while also being "one-shot", in that they use only one copy of an entangled resource state. The optimization is in the sense of minimizing the amount of entanglement used, and it is often the case that less entanglement is needed than with an alternative protocol using two-way teleportation.
We propose and study a method for using non-maximally entangled states to implement probabilistically non-local gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequences, the method becomes more efficient at a certain range of parameters. Gates of the form $\exp[iξσ_{n_A}σ_{n_B}]$ with $ξ\ll1$, can be implemented with nearly unit probability and with vanishingly small entanglement, while for the distillation-based method the gate is produced with a vanishing success probability. We also derive …
Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order
本文提出了一种基于不定因果顺序的实用协议，实现任意受控单元arity门，通过调整单量子比特操作减少电路复杂度并提高实验灵活性。
Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain tim…
Nonlocal continuous-variable gates by amplified optical connections
提出利用光学参量放大器实现两个远程用户间的非局域连续变量量子非破坏门，提升纠缠能力和抑制噪声，适用于分布式量子计算。
We develop the probabilistic implementation of a nonlocal gate $\exp{[iξ{σ_{n_A}}σ_{n_B}]}$ and $ξ\in[0,\frac\pi4]$, by using a single non-maximally entangled state. We prove that, nonlocal gates can be implemented with a fidelity greater than 79.3% and a consumption of less than 0.969 ebits and 2 classical bits, when $ξ\leq0.353$. This provides a higher bound for the feasible operation compared to the former techniques \cite{Cirac,Groisman,Bennett-1}. Besides, gates with $ξ\geq0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency a…
Tunable Nonlocal $ZZ$ Interaction for Remote Controlled-Z Gates Between Distributed Fixed-Frequency Qubits
本文提出一种分布式硬件架构，通过双超导耦合器抑制残余静态模块耦合，实现高保真度的远程受控Z门，验证了其在超导处理器中的可行性。
In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising properties: 1) simulating it with the assistance of unlimited EPR pairs requires far more communication than with a better choice of entangled state, and 2) its communication capacity is far lower than its capacity to create entanglement. This suggests that 1) unlimited EPR pairs are not the most general model of entanglement assistance for two-party communication…
Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of non-local properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-bit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can …
Low-rank geometry of two-qubit gates
本文基于两量子比特门的行列式几何，结合Weyl室表示与算子Schmidt理论，将门合成视为距离问题，量化非局域复杂性，并展示iSWAP门是接近局部操作的最完美纠缠门。
Uncertainty principle is one of the central concepts in quantum theory. Different forms of this particular principle have been discoursed in various foundational and information theoretic topics. In the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by fine-grained uncertainty relation. On the other hand, in continuous variable paradigm Robertson-Schrodinger (RS) uncertainty relation has been used to detect multi-mode entanglement. Here we show that RS uncertainty relation plays an important role to discriminate between quantum and post-quantu…
Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish similar result by using device independent success probability of Hardy's nonlocality argument for tripartite quantum system. We construct an example of a tri-partite Hardy correlation which is post-quantum but satisfies not only all bipartite information principle but also the GYNI inequality.
The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum …
A Path-Superposition Framework for Quantum Gate Teleportation
介绍基于路径叠加的确定性量子门隐形传态通用框架，通过预共享最大纠缠资源相位和路径依赖局部酉算子指定目标非局部操作，给出设计条件并构建协议，还概述了光子实现方案。
We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e. no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria…
We propose a simple setup for the conversion of multipartite entangled states in a quantum network with restricted access. The scheme uses nonlocal operations to enable the preparation of states that are inequivalent under local operations and classical communication, but most importantly does not require full access to the states. It is based on a flexible linear optical conversion gate that uses photons, which are ideally suited for distributed quantum computation and quantum communication in extended networks. In order to show the basic working principles of the gate, we focus on converting…
We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a,…
Post-quantum nonlocality in the minimal triangle scenario
本文研究了无输入且输出为二值的最小三角形场景中的网络非定域性，通过具体实例证明其支持与无信号传输及源独立性相容但不兼容独立量子或经典源的非定域关联，该性质对噪声鲁棒，并识别出等价的 PR box。
Incompatibility assisted Zeno-like confinement enables unbounded sharing of nonlocality
研究无界数量副本顺序共享贝尔非局域性的条件，通过不相容测量提取非局域性，后处理态保持非局域，建立两种测量场景下初始态和测量噪声选择的约束，证明渐近极限下副本后处理态近似相同。
We show that families of Instantaneous Quantum Polynomial (IQP) circuits corresponding to nontrivial Bell tests exhibit nonlocality. However, we also prove that this nonlocality can only be demonstrated using post-selection or nonlinear processing of the measurement outcomes. Therefore if the output of a computation is encoded in the parity of the measurement outcomes, then families of IQP circuits whose full output distributions are hard to sample still only provide a computational advantage relative to locally causal theories under post-selection. Consequently, post-selection is a crucial te…
Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron within which perfect entanglers form a polyhedron. On the other hand, it is known from the later decomposition that Schmidt number of nonlocal gates can be either 2 or 4. In this work, some aspects of later decomposition are investigated. It is shown that two gates differing by local operations possess same set of Schmidt coefficients. Employing geometrical…
Nonlocal photonic quantum gates over 7.0 km
本研究利用复用量子存储器、电信波长飞行量子比特及光纤前馈控制，首次在7公里间距的节点间实现非局域光子量子门，并验证量子并行算法，为城域分布式量子网络构建奠定基础。
Bounds on Instantaneous Nonlocal Quantum Computation
本文研究瞬时非局域量子计算，提出LOBC协议，实现任意两量子比特门仅需O(log(1/ε))个纠缠比特，较LOCC指数改进，并首次给出基于纠缠熵的下界。
Entanglement and nonlocality are studied in the framework of pre-/post-selected ensembles with the aid of weak measurements and the Two-State-Vector Formalism. In addition to the EPR-Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose pre- or post-selected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting "emerging correlations" between independent pre- and post-selected ensembles of particles. This can be viewed as a quantum violation of the classical "pigeonhole principle".
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…
Instantaneous nonlocal quantum computation and circuit depth reduction
本研究针对瞬时两方量子计算，证明花园软管装置无法显著降低纠缠成本，并提出任何酉电路可被深度与T深度成正比的测量电路实现，讨论了其局限与扩展。
Post-selection games
本文提出后选择游戏，通过允许裁判舍弃轮次，扩展了非本地游戏，以更有效地分析低检测效率的贝尔测试。
We study the class of two qubit gates which can be achieved using only linear optical elements (beam splitters and phase shifters) and post-selection. We are able to exactly characterize this set, and find that it is impossible to implement most two qubit gates in this way. The proof also gives rise to an algorithm for calculating the optimal success probability of those gates which are achievable.
Parallel distributed quantum gates for dual-species quantum emitters
本文提出一种并行协议，用于在空间分离的双物种量子发射器中实现非局域量子门，利用纠缠光子对作为量子数据总线，实现高效分布式量子计算。
We show that a beam splitter of reflectivity one-third can be used to realize a quantum phase gate operation if only the outputs conserving the number of photons on each side are post-selected.
High-fidelity entangling gates and nonlocal circuits with neutral atoms
该研究通过中性原子量子处理器实现了高保真的CZ纠缠门，利用状态选择性读取和量子比特重用技术，提高了保真度并展示了低误差量子电路在非本地纠缠态研究中的应用。
When Mei-Gu Guan's 1960 Postmen Get Empowered with Bell's 1964 Nonlocal Correlations, or, Nonlocal Advantage in Vehicle Routing Problem
本文研究贝尔非局域关联如何为多邮递员车辆路径问题提供成本优化优势，首次将量子纠缠引入交通路径优化，拓展了非局域关联在组合优化与运筹学中的应用。
The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus, it is natural to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination strategies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurrence of NLWE in …
Recently it was realized that linear optics and photo-detectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation (eLOQC) was to design a simple non-deterministic gate, which upon post-selection based on a measurement result implements a non-linear phase shift on one mode. Here a computational strategy is given for finding non-deterministic gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained.
Universal multiport interferometers for post-selected multi-photon gates
本文提出利用通用多端口干涉仪、双轨路径编码、辅助路径和单光子后选择构造受控-Z与受控-受控-Z光子门，并提高其成功概率，揭示Reck和Clements方案超越玻色采样的能力。
We present an efficient way for measuring the entanglement of the atoms. Through the auxiliary single photons input-output process in cavity quantum electrodynamics (QED), the concurrence of the atomic entanglement can be obtained according to the success probability of picking up the singlet states of the atoms. This protocol has three advantages: First, we do not require the sophisticated controlled-not (CNOT) gates. Second, the distributed atoms are not required to intact with each other. Third, the atomic entanglement can be distributed nonlocally, which provides its important applications…
This paper studies secure multiparty quantum computation (SMQC) without nonlocal measurements. Firstly, this task is reduced to secure two-party quantum computation of nonlocal controlled-NOT (NL-CNOT) gate. Then, in the passive adversaries model, the secure computation of NL-CNOT is reduced to bit commitment. Thus, a SMQC scheme can be constructed based on bit commitment. This scheme does not depend on trusted third party, and is secure in the passive adversaries model. It is also pointed out that a vulnerability exists in any secure two-party quantum computation protocol of NL-CNOT gate.
Frequency-Multiplexed Parallel Gates for Quantum LDPC Codes in a Two-Dimensional Ion Crystal
针对量子LDPC码症候测量需非局域纠缠门的问题，提出频分复用方案实现二维离子晶体上的并行非局域纠缠门，通过绝热条件优化后可达到10^-12的逻辑错误率。
Quantum nonlocal correlations of anomalous weak values
研究后选择下CHSH算符反常弱值作为非局域关联的广义界，发现后选择和纠缠是不同资源，纠缠是超越可分离后选择界的关键，并给出纠缠见证协议。
Tight Limits on Nonlocality from Nontrivial Communication Complexity; a.k.a. Reliable Computation with Asymmetric Gate Noise
该研究通过两项基于可靠经典计算新见解的结果，探讨了“通信复杂度非平凡”作为量子力学信息论公理的可行性，指出其不足以刻画CHSH关联。
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. In this article I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics.
We propose a scheme to achieve quantum computation with neutral atoms whose interactions are catalyzed by single photons. Conditional quantum gates, including an $N$-atom Toffoli gate and nonlocal gates on remote atoms, are obtained through cavity-assisted photon scattering in a manner that is robust to random variation in the atom-photon coupling rate and which does not require localization in the Lamb-Dicke regime. The dominant noise in our scheme is automatically detected for each gate operation, leading to signalled errors which do not preclude efficient quantum computation even if the err…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two…
We propose a scheme for linear optical quantum Fredkin gate based on the combination of recently experimentally demonstrated linear optical partial SWAP gate and controlled-Z gates. Both heralded gate and simplified postselected gate operating in the coincidence basis are designed. The suggested setups have a simple structure and require stabilization of only a single Mach-Zehnder interferometer. A proof-of-principle experimental demonstration of the postselected Fredkin gate appears to be feasible and within the reach of current technology.
Recently, it was shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and quantum counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by a new rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of success probability of NS-gate with a new post-selection measurement. The id…
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k$'th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective $k$-body interactions using Hamil…
Photonic Simulation of Beyond-Quantum Nonlocal Correlations (e.g. Popescu-Rohrlich Box) with Non-Signaling Quantum Resources
本文提出利用本质非信号的物理资源与系统间动力学关联模拟 Popescu-Rohrlich 等超量子非局域关联，并在四量子比特光子平台上验证。
Circuit knitting with classical communication
本文研究基于准概率模拟的电路编织方法，证明在子电路间引入经典通信可将含 $n$ 个非局域 CNOT 门的模拟开销从 $O(9^n)$ 降至 $O(4^n)$，并推广到一般 Clifford 门及部分其他门。
Parallel two-qubit entangling gates via a quantum nondemolition interaction controlled by rotation
本文提出一种基于量子非破坏性相互作用和正交分量旋转的协议，利用多模自由度实现多个双量子比特系统的并行操作，并通过等价类形式体系证明其能以1/3概率实现非局域$SWAP$和纠缠$\sqrt{SWAP}$操作。
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