S. Sensarn, G. Y. Yin, S. E. Harris
We demonstrate a new type of quantum mechanical correlation where phase modulators at distant locations, acting on the photons of an entangled pair, interfere to determine the apparent depth of modulation. When the modulators have the same phase, the modulation depth doubles; when oppositely phased, the modulators negate each other.
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Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of $2\times2$ Hilbert space. The quantum nonlocality persists longer in $2\times2$ Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered enta…
This is to reply to Cereceda's comment on "Quantum nonlocality for a three-particle nonmaximally entangled state without inequaltiy"
Nonlocal correlations as revealed by the violations to Bell inequalities are incompatible with local models without any nonlocal correlations. However some tripartite entangled states, e.g., symmetric pure states, exhibit a stronger nonlocality even incompatible with hybrid local/nonlocal models allowing nonlocal correlations between any two parties. Here we propose a three-particle Hardy-type test without inequality, as illustrated by a gedanken experiment, that is failed by all non-signaling local models while is passed by all tripartite entangled asymmetric pure states. Our result implies t…
We present a variation on a gedanken experiment of Hardy [Phys. Rev. Lett. 68 (1992) 2981] that allows, for the first time, a Hardy-type nonlocality proof for two maximally entangled particles in a four-dimensional Hilbert space.
Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett. \textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 \otimes 2 \otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but l…
We study the feasibility of nonlocally compensating for polarization mode dispersion (PMD), when polarization entangled photons are distributed in fiber-optic channels.We quantify the effectiveness of nonlocal compensation while taking into account the possibility that entanglement is generated through the use of a pulsed optical pump signal.
In a recent Brief Report, Zheng [S-B. Zheng, PRA 66, 014103 (2002)] has given a proof of nonlocality without using inequalities for three spin-1/2 particles in the nonmaximally entangled state |psi> = cosθ|+++> + i sinθ|-->. Here we show that Zheng's proof is not correct. Indeed it is the case that, for the experiment considered by Zheng, the only state that admits a nonlocality proof without inequalities is the maximally entangled state.
We consider entangled two-photon generalized binomial states of the electromagnetic field in two separate cavities. The nonlocal properties of this entangled field state are analyzed by studying the electric field correlations between the two cavities. A Bell's inequality violation is obtained using an appropriate dichotomic cavity operator, that is in principle measurable.
For the 3-qubit UPB state, i.e., the bound entangled state constructed from an Unextendable Product Basis of Bennett et al. (Phys. Rev. Lett. 82:5385, 1999), we provide a set of violations of Local Hidden Variable (LHV) models based on the particular type of reflection symmetry encoded in this state. The explicit nonlocal unitary operation needed to prepare the state from its reflected separable mixture of pure states is given, as well as a nonlocal one-parameter orbit of states with Positive Partial Transpositions (PPT) which swaps the entanglement between a state and its reflection twice dur…
Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequali…
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states which admit a fully local hidden variable model, i.e. where all parties are separated. Hence, although these states are entangled in the strongest possible sense, they cannot lead to Bell inequality violation considering general non-sequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing …
We consider ramifications of the use of high speed light modulators to questions of correlation and measurement of time-energy entangled photons. Using phase modulators, we find that temporal modulation of one photon of an entangled pair, as measured by correlation in the frequency domain, may be negated or enhanced by modulation of the second photon. Using amplitude modulators we describe a Fourier technique for measurement of biphoton wave functions with slow detectors.
A pair of optical pulses traveling through two dispersive media will become broadened and, as a result, the degree of coincidence between the optical pulses will be reduced. For a pair of entangled photons, however, nonlocal dispersion cancellation in which the dispersion experienced by one photon cancels the dispersion experienced by the other photon is possible. In this paper, we report an experimental demonstration of nonlocal dispersion cancellation using entangled photons. The degree of two-photon coincidence is shown to increase beyond the limit attainable without entanglement. Our resul…
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state rho of two d-dimensional systems and completely depolarized noise, with respective weights p and 1-p. We first construct a local model for the case in which rho is maximally entangled and p at or below a certain bound. We then extend the model to arbitrary rho. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements, the critical value of the noise parameter p for which the state becomes local is at least asymptoticall…
All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
针对源自稳定子形式的多体态系统，本文建立真正纠缠与真正非局域性的等价关系，证明真正纠缠稳定子子空间上的态为多体完全非局域，并推导任意多体态真正非局域性含量下界，为实验估计奠定基础。
All pure entangled states can lead to fully nonlocal correlations
本文研究了纯纠缠态的非局域性，证明了非最大纠缠态也能产生完全非局域相关性，并探讨了其在多复制场景中的表现。
Standard quantum cryptographic protocols are not secure if one assumes that nonlocal hidden variables exist and can be measured with arbitrary precision. The security can be restored if one of the communicating parties randomly switches between two standard protocols.
All Entangled States are Nonlocal and Self-Testable in the Broadcast Scenario
该研究证明在广播场景中，所有纠缠态均为非本地且可自测，揭示了量子理论中纠缠与非本地性的关系。
One-way network nonlocality of continuous variable entangled networks
针对非经典性局限于离散变量量子网络的问题，提出首个允许单向经典通信的全光连续变量量子网络非定域性验证方法，实现了首个验证该网络量子关联的设备无关方法。
Entanglement and wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using Weak Values, was demonstrated by Lundeen et al., Nature \textbf{474}, 188(2011). However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element since that requires obtaining the Weak Values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using Modular Values. The method is …
We suggest and demonstrate a scheme for coherent nonlocal compensation of pure phase objects based on two-photon polarization and momentum entangled states. The insertion of a single phase object on one of the beams reduces the purity of the state and the amount of shared entanglement, whereas the original entanglement can be retrieved by adding a suitable phase object on the other beam. In our setup polarization and momentum entangled states are generated by spontaneous parametric downconversion and then purified using a programmable spatial light modulator, which may be also used to impose a…
Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, here we study the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled qua…
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…
Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but …
Genuinely entangled subspaces and strongly nonlocal unextendible biseparable bases in four-partite systems
本文研究四量子比特系统中真正纠缠子空间的构建，证明其强非局域性并展示其在所有双分拆上的可蒸馏性，为量子信息处理提供理论基础。
Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the nonlocality present in a single particle from an entangled pair using the method of weak measurements [Phys. Rev. Lett. {\bf 114}, 250401 (2015)]. Here we report an observation of double CHSH…
Quantum entanglement and quantum nonlocality of $N$-photon entangled states $|ψ_{N m}> =\mathcal{N}_{m}[\cosγ|N-m>_{1}|m>_{2} +e^{iθ_{m}}\sinγ|m>_{1}|N-m>_{2}]$ and their superpositions are studied. We indicate that the relative phase $θ_{m}$ affects quantum nonlocality but not quantum entanglement for the state $|ψ_{N m}>$. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of $|ψ_{N m}>$, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal valu…
Nonlocality as a fundamental aspect of quantum mechanics is witnessed by violation of Bell inequality or its variants, for which all relevant studies assume some correlations exhibited by local realistic theories. The strategy of Bell's theorem is to establish some criteria to distinguish local realistic theories from quantum mechanics with respect to the nonlocal nature of entangled systems. Here we propose a model independent study of nonlocality that needs not to assume any local theory since observation of the expected nonlocal effect is straightforward quantum mechanically. Our proposal i…
It is shown that it is possible to rule out all local and stochastic hidden variable models accounting for the quantum mechanical predictions implied by almost any entangled quantum state vector of any number of particles whose Hilbert spaces have arbitrary dimensions, without resorting to Bell-type inequalities. The present proof makes use of the mathematically precise notion of Bell locality and it involves only simple set theoretic arguments.
We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of th…
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
Hardy nonlocality for entangled pairs in a four-particle system
本研究探讨四粒子环状纠缠结构中Hardy非局域性的增强效应，通过量子电路模拟与实验验证，发现其相比完全纠缠系统具有更强的非局域性矛盾条件。
Nonlocal phase modulation of multimode, continuous-variable twin beams
实验研究多模连续变量孪生光束的非局域相位调制，通过电光调制器在热铷蒸气四波混频产生的纠缠光束上实现，发现非局域调制可产生频率模式间的量子关联。
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Though Bell nearly showed a violation using the CHSH inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he doesn't give a quantitative estimation of the maximum achievable violation for the wavefunction he considers. In this article, we show how his strategy can be reimagined using the transv…
Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
本文提出一个充分条件，用于构造高维真正纠缠子空间，发现最大已知的GES，并证明所有状态在任意双分区下1可蒸馏，同时证明UBB在LOCC下不可区分。
Decidability of fully quantum nonlocal games with noisy maximally entangled states
针对共享含噪最大纠缠态的完全量子非局部博弈，本文证明逼近其量子值可判定，并通过超算子 Fourier 分析给出所需态份数的可计算上界。
Maximally entangled states are not complete for pseudo-telepathy
该研究针对量子非局域性领域的长期开放性问题，构造了输入集大小为4和3、输出集均为6的双体内积游戏，作为最大纠缠态对于伪心灵感应游戏不完备的反例，证明了最大纠缠态并非此类游戏的完备资源。
Quantum nonlocality is arguably among the most counter-intuitive phenomena predicted by quantum theory. In recent years, the development of an abstract theory of nonlocality has brought a much deeper understanding of the subject. In parallel, experimental progress allowed for the demonstration of quantum nonlocality in a wide range of physical systems, and brings us close to a final loophole-free Bell test. Here we combine these theoretical and experimental developments in order to explore the limits of quantum nonlocality. This approach represents a thorough test of quantum theory, and could …
Recently the authors in [Phys. Rev. Lett. 125, 090401 (2020)] considered the following scenario: Alice and Bob each have half of a pair of entangled qubit state. Bob measures his half and then passes his part to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice.…
The hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but in general do not maximally violate, Bell's inequality due to Clauser, Horne, Shimony and Holt. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum information processing including quantum teleportation, entangle…
We consider a general version of the phenomenon of more nonlocality with less entanglement, within the framework of the unambiguous (i.e., conclusive) quantum state discrimination problem under local quantum operations and classical communication. We show that although the phenomenon was obtained before for two qutrits, it can also be observed for two qubits, while still being at the single-copy level. We establish that the phenomenon is intrinsically connected to the concept of unextendible entangled bases, in the two-qubit case. In the process, we demonstrate a hierarchy of nonlocality among…
We assess quantum non-locality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger (GHZ), W and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditio…
Nonlocal nonstabilizerness for slightly entangled quantum many-body states
研究轻微纠缠量子多体状态的非局域非稳定性，提出施密特参考态框架，通过排序后的施密特谱直接构建取代局部酉变换上的高度非凸优化，支持非局域稳定器雷尼熵推测，表明该框架能有效获取弱纠缠多体状态的非局域非稳定性。
Increasingly sophisticated quantum computers motivate the exploration of their abilities in certifying genuine quantum phenomena. Here, we demonstrate the power of state-of-the-art IBM quantum computers in correlation experiments inspired by quantum networks. Our experiments feature up to 12 qubits and require the implementation of paradigmatic Bell-State Measurements for scalable entanglement-swapping. First, we demonstrate quantum correlations that defy classical models in up to nine-qubit systems while only assuming that the quantum computer operates on qubits. Harvesting these quantum adva…
We show that the continuous-variable analogues to the multipartite entangled Greenberger-Horne-Zeilinger states of qubits violate Bell-type inequalities imposed by local realistic theories. Our results suggest that the degree of nonlocality of these nonmaximally entangled continuous-variable states, represented by the maximum violation, grows with increasing number of parties. This growth does not appear to be exponentially large as for the maximally entangled qubit states, but rather decreases for larger numbers of parties.
We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum stat…
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.
Noise-robust proofs of quantum network nonlocality
针对量子网络非定域性证明局限于理想化情形的问题，提出基于近似刚性结果的噪声鲁棒证明方法，可处理任意噪声，示例中退相干噪声鲁棒性达80%、白噪声达0.5%，为实际实现提供前景。
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculatin…
Quantum nonlocality of several four-qubit states is investigated by constructing a new Bell inequality. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, cluster state, and the state $|χ>$ that has been recently proposed in [PRL, {\bf 96}, 060502 (2006)]. The Bell inequality is optimally violated by $|χ>$ but not violated by the GHZ state. The cluster state also violates the Bell inequality though not optimally. The state $|χ>$ can thus be discriminated from the cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by consideri…
Nonlocal correlations are useful for device independent (DI) randomness certification [Nature (London) {\bf 464}, 1021 (2010)]. The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here w…
A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory --- a fact that is demonstrated by the quantum violation of Bell inequalities. The precise relationship between quantum entanglement and the violation of Bell inequalities is, however, not well understood. While it is known that entanglement is necessary for such a violation, it is not clear whether all entangled states violate a Bell inequality, even in the scenario where one allows joint operations on multiple copies of the state and loc…
In this paper, we provide a simple but powerful module to generate entangled qudits. This module assisted with cross-Kerr nonlinearity is available to the entangled qudits generation with arbitrary dimension, and it could work well even when the two independent qudits lose the same number of single photons. Moreover, with the cascade uses of modules, the deterministic generation but with nonidentical forms of entangled qudits is possible.
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that the correlations observed for some entangled quantum states can be explained within the framework of local models, thus proving that these resources are inequivalent in this scenario. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not disp…
The possibility of nonlocal quantum communication is considered. We investigate three $gedankenexperiments$ that have variable entanglement: (1) a 4-detector polarization-entangled system, (2) a 4-detector path-entangled system, and (3) a 3-detector path-entangled system that uses an innovative optical mixer to combine photon paths. A new quantum paradox is reviewed in which the presence or absence of an interference pattern in a path-entangled two photon system, controlled by measurement choice, is a potential nonlocal signal. We show that for the cases considered, even when interference patt…
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite e…
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely projective measurements. Here we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements (POVMs), and show that the states violate a Bell inequality after local filtering. Hence there exist entangled states, the nonl…
Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally…
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