Experimental entangled entanglement

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement."     

Quantum Entanglement of Many Distant Bose-Einstein Condensates in an Optical Lattice by Interference

We propose a scheme to generate maximally entangled states of two distant Bose-Einstein condensates, which are trapped in different potential wells of a one-dimensional optical lattice. We show how such maximally entangled state can be used to test the Bell inequality and realize quantum teleportation of a Bose-Einstein condensate state. The scheme proposed here is based on the interference of Bose-Einstein condensates leaking out from different potential wells of optical lattice. It is briefly pointed out that this scheme can be extended to generate maximally entangled Greenberger-Horne-Zeilinger (GHZ) states of 2m (m >1) distant Bose-Einstein condensates.     

A Three-Qubit State Entanglement Concentration Protocol Assisted by Two-Qubit Systems

In this paper we present an entanglement concentration protocol for enhancement of the amount of entanglement maximally in a three qubit non-maximally entangled state. We use a Bell state for this purpose. Here the speciality is that no non-local measurement involving more than one parties is involved in the protocol. It is shown that for obtaining best probability of success a maximally entangled Bell state must be used. The probability of success in our protocol increases with an increase in the amount of entanglement in the assisting Bell state, and is zero when the entanglement vanishes.     

From Quantum State Targeting to Bell Inequalities

Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally entangled states. The optimal solution of the game is used to derive a Bell inequality for two entangled qutrits. We argue that the nice properties of the inequality are direct consequences of the method of construction.     

Postselective measurement of the electronic entanglement in the system of two Mach-Zehnder interferometers with coulomb interaction

The parameters at which the maximally entangled two-particle state appears in the system of two ideal electronic Mach-Zehnder interferometers are known. In this work, the operation of nonideal devices with finite scattering in splitters and with reflection in the region of the Coulomb Interaction has been considered. It has been shown that, under the condition of postselection of experimental results, these factors can increase the observed Bell parameter to values exceeding Cirel’son’s (or Tsirelson’s) bound equal to 2√2 up to the mathematical limit equal to 4. A simple postselective measurement scheme providing B = 4 has been described. Although the results of such measurements are not as fundamental as the observation of the violation of Bell’s inequality, they can indirectly indicate the existence of an entangled state in the system. The measurement system is more stable against fluctuations of the phase than a system without postselection. Furthermore, it has been found that the proposed system is optimal for investigation of cross correlations between interferometers in the dc regime (beyond the paradigm of the violation of Bell’s inequality) because they cannot be generated by coordinated fluctuations of Aharonov-Bohm phases.     

Analysis of elliptically polarized maximally entangled states for bell inequality tests

When elliptically polarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.     

Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy, and random outcomes are thus highly desired properties for genuine-multipartite cryptographic scenarios. We prove that local measurements on any Greenberger-Horne-Zeilinger state can produce correlations that are fully genuine-multipartite nonlocal, monogamous, and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss applications to device-independent secret sharing.     

Optimal bell tests do not require maximally entangled states

Any Bell test consists of a sequence of measurements on a quantum state in spacelike separated regions. Thus, a state is better than others for a Bell test when, for the optimal measurements and the same number of trials, the probability of existence of a local model for the observed outcomes is smaller. The maximization over states and measurements defines the optimal nonlocality proof. Numerical results show that the required optimal state does not have to be maximally entangled.     

Maximally nonlocal and monogamous quantum correlations

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes and use it to give a simple proof that the maximally entangled state of two d-dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental program to obtain as good an upper bound as possible on the fraction of local states and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among nonsignaling correlations and, hence, can be used for quantum key distribution secure against postquantum (but nonsignaling) eavesdroppers.     

A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement

Suppose that Alice and Bob make local two-outcome measurements on a shared entangled quantum state. We show that, for all positive integers d, there exist correlations that can only be reproduced if the local Hilbert-space dimension is at least d. This establishes that the amount of entanglement required to maximally violate a Bell inequality must depend on the number of measurement settings, not just the number of measurement outcomes. We prove this result by establishing a lower bound on a new generalization of Grothendieck’s constant.     

Projection of two biphoton qutrits onto a maximally entangled state

Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems with three states (qutrits) onto a generalized maximally entangled state. Each qutrit is represented by the polarization of a pair of indistinguishable photons-a biphoton. The projection is a joint measurement on both biphotons using standard linear optics elements. This demonstration enables the realization of quantum information protocols with qutrits, such as teleportation and entanglement swapping.     

Towards Loophole-Free Optical Bell Test of CHSH Inequality

Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.     

State-Independent Proofs of Bell's Theorem Without Inequalities and Bell Inequality for Four-Qubit System

A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which possesses two qubits, is proposed. It is different from the other proofs in which there exists a fundamental requirement that certain specific suitable Bell states have been chosen. Moreover, in any non-ideal situation, a common Bell inequality independent of the choices of the 16-product states is derived, which is used to test the contradiction between quantum mechanics and local reality theory in the reach of current experimental technology.     

All bipartite entangled States display some hidden nonlocality

One of the most significant and well-known properties of entangled states is that they may lead to violations of Bell inequalities and are thus inconsistent with any local-realistic theory. However, there are entangled states that cannot violate any Bell inequality, and in general the precise relationship between entanglement and observable nonlocality is not well understood. We demonstrate that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all entangled states. Our proof of the result consists of two main steps. We first provide a simple characterization of the set of states that do not violate the CHSH inequality even after general local operations and classical communication. Second, we prove that for each entangled state sigma, there exists another state rho not violating the CHSH inequality, such that rhomultiply sign in circlesigma violates the CHSH inequality.     

Nonlocality and Multipartite Entanglement in Asymptotically Flat Space-Times

We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time.For two qubit case,we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions.On the other hand,for those observers in the causally disconnected regions inequality is not violated for any values of acceleration.The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle.For a three qubit state,the inequality violated for measurements done by both causally connected and disconnected observers.Initially GHZ state with non zero 3-tangle,in accelerated frame,transformed to a four qubit state with vanishing 4-tangle value.On the other hand,for a W-state with zero 3-tangle,in non inertial frame,transformed to a four qubit state with a non-zero 4-tangle acceleration dependent.In an expanding space-time with asymptotically flat regions,for an initially maximally entangled state,the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation.For some initially maximally entangled states,the generated four qubit state due to expansion of space-time,has non vanishing 4-tangle.     

Large Violation of Bell Inequalities with Low Entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order \({\frac{\sqrt{n}}{\log n}}\) with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.     

Logic Bell state concentration with parity check measurement

Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.     

Testing the nonlocality of entangled states by a new Bell-like inequality

We test a new four-qubit entangled state by the former Bell-like inequalities and find that it violates these inequalities, but not maximally. According to this entangled state, we build a new Bell-like inequality, which is violated by this new state maximally. We also determine the nonlocality of some other four-qubit states by the new inequality. It is found that the new inequality acts as a strong entanglement witness for the new state. This can be used to test new entangled states experimentally.     

Ontological Models,Preparation Contextuality and Nonlocality

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some \(\psi \) -epistemic models without any use of Bell’s inequality. In particular, nonlocality of a non maximally \(\psi \) -epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.