Bell Inequality Tests Research Articles

Subdecoherence time generation and detection of orbital entanglement in quantum dots.

Recent experiments have demonstrated subdecoherence time control of individual single-electron orbital qubits. Here we propose a quantum-dot-based scheme for generation and detection of pairs of orbitally entangled electrons on a time scale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, providing for an unambiguous short-time Bell inequality test of orbital entanglement.

Bell-inequality tests using asymmetric entangled coherent states in asymmetric lossy environments

We study an asymmetric form of two-mode entangled coherent state (ECS), where the two local amplitudes have different values, for testing the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We find that the asymmetric ECSs have obvious advantages over the symmetric form of ECSs in testing the Bell-CHSH inequality. We further study an asymmetric strategy in distributing an ECS over a lossy environment and find that such a scheme can significantly increase violation of the inequality.

Atomic Hong-Ou-Mandel experiment.

Two-particle interference is a fundamental feature of quantum mechanics, and is even less intuitive than wave-particle duality for a single particle. In this duality, classical concepts--wave or particle--are still referred to, and interference happens in ordinary space-time. On the other hand, two-particle interference takes place in a mathematical space that has no classical counterpart. Entanglement lies at the heart of this interference, as it does in the fundamental tests of quantum mechanics involving the violation of Bell's inequalities. The Hong, Ou and Mandel experiment is a conceptually simpler situation, in which the interference between two-photon amplitudes also leads to behaviour impossible to describe using a simple classical model. Here we report the realization of the Hong, Ou and Mandel experiment using atoms instead of photons. We create a source that emits pairs of atoms, and cause one atom of each pair to enter one of the two input channels of a beam-splitter, and the other atom to enter the other input channel. When the atoms are spatially overlapped so that the two inputs are indistinguishable, the atoms always emerge together in one of the output channels. This result opens the way to testing Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, and to testing theories of the quantum-to-classical transition. Our work also demonstrates a new way to benchmark non-classical atom sources that may be of interest for quantum information processing and quantum simulation.

Using weak values to experimentally determine “negative probabilities” in a two-photon state with Bell correlations

Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing a joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such a distribution experimentally, as a set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to a quantum probe, however, produces minimal back-action, and so enables a weak measurement of the projector of one observable, followed by a projective measurement of a non-commuting observable. By this technique it is possible to empirically measure weak-valued probabilities for all of the values of the observables relevant to a Bell test. The marginals of this joint distribution, which we experimentally determine, reproduces all of the observable quantum statistics including a violation of the Bell inequality, which we independently measure. This is possible because our distribution, like the weak values for projectors on which it is built, is not constrained to the interval [0, 1]. It was first pointed out by Feynman that, for explaining singlet-state correlations within "a [local] hidden variable view of nature ... everything works fine if we permit negative probabilities". However, there are infinitely many such theories. Our method, involving "weak-valued probabilities", singles out a unique set of probabilities, and moreover does so empirically.

Entanglement: A Contrarian View

Entanglement is defined in terms of some kind of instantaneous interaction, contrary to the relativistic principle that all interaction is possible only at a velocity less than that of light. This conflict with an otherwise inviolate principle justifies re-examination of the arguments leading to its (ostensible) rejection. Herein the historically essential notion, namely wave-collapse by measurement or the “Projection Hypothesis” of von Neumann is brought to attention and seen to violate Popper’s Principle of negatability; thereby disqualifying it as a scientific proposition. Further, it is observed that polarization of electromagnetic signals as used in experiments testing Bell Inequalities is described by structure excluding quantum principles. Consequently, most experiments taken to verify Bell’s conclusions cannot in principle do so: a quantum effect cannot be found where there is no quantum structure. Finally, a simple simulation which demonstrates the classical (electromagnetic) generation of the data that violates a Bell Inequality, thereby proving by counterexample that Bell’s so-called theorem is misunderstood, is presented.

Linear optics schemes for entanglement distribution with realistic single-photon sources

We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton "tail" are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee generation of entanglement in the relevant qubit subspaces and compare it with classicality criteria. We also quantify the amount of entanglement that can be produced with imperfect single-photon sources, optimized over setup parameters, using as a measure entanglement of formation. Finally, we discuss verification of the generated entanglement by testing Bell's inequalities. The analysis is carried out for two schemes. The first one is the well-established one-photon scheme, which produces a photon in a delocalized superposition state between two nodes, each of them fed with one single photon at the input. As the second scheme, we introduce and analyze a linear-optics analog of the robust scheme based on interfering two Stokes photons emitted by atomic ensembles, which does not require phase stability between the nodes.

Towards loophole-free Bell inequality test with preselected unsymmetrical singlet states of light

Can a Bell test with no detection loophole be demonstrated for multi-photon entangled states of light within the current technology? We examine the possibility of a postselection-free CHSH-Bell inequality test wih an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed to be not useful for this purpose.

Violation of the Bell–Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states

We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.

Testing Bell's inequality using charmonium decays

This paper discusses the feasibility of testing Bell's inequality with the charmonium decays \eta_c -> \Lambda \Lambda, \chi_{c0} -> \Lambda\Lambda and J/\Psi -> \Lambda\Lambda. We develop a new formulation of the Bell's inequality represented with particles' momenta which can be measured definitely in experiment and seek if it violates in these decays. It is illustrated that the \eta_c channel and the \chi_{c0} channel maximally violate Bell's inequality, while the J/\Psi channel gives no inconsistency with it. Simulations dealing with experimental aspects are also implemented. The expected statistical fluctuations and achievable significance are estimated as a function of sample size.

Violation of Bell--CHSH--CH Inequalities by Superposition of Two Coherent States (π/2 Out of Phase)

Einstein et al. [1] realized that in many states, when measuring either linear momentum or position of one of the two particles, one can infer precisely either momentum or position of the other. They advocated that if the local realism is taken for granted, then quantum theory is an incomplete description of the physical world. Following this line, Bell demonstrated that a contradiction arises between the EPR assumptions of realism and locality and quantum physics and termed as Bell's theorem. Quantum nonlocality con rms the interpretation and validity of quantum mechanics against the local-realistic theories by violations of the constraints on the correlation between local measurement outcomes. Mathematical expression of such a constraint is known as Bell inequality [2], of which many variants exist [3 5]. For example, well known Clauser, Horne, Shimony, and Holt (CHSH) inequality [3] and Clauser and Horne (CH) [4] are used for the veri cation of nonlocal correlations in a two-dimensional Hilbert space. The Bell inequalities concern measurements made by observers on pairs of particles that have interacted and then separated. According to the quantum mechanics they are entangled, while local realism would limit the correlation of subsequent measurements of the particles. Nonlocal correlations play crucial role for the device-independent versions of quantum information protocols, such as cryptography, random number generation, state estimation, and entangled measurement certi cation. Quantum continuous variables (CV) [6] of light have been successfully used to realize some of the standard informational tasks traditionally based on qubits. Bell-inequality tests were performed by using qubits [7] which satisfy the space-like separation between two local parties. But, the di culty of the detection loophole [8, 9] demanded to look at other approaches for Bell-inequality tests. Continuous variable (CV) states are of recent in-

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states for Bell-inequality tests are studied theoretically. By utilizing the method of photon-parity measurement, it is found that photon addition can always increase the degrees of Bell violations within a certain parameter range. A possible scheme for generating photon-added squeezed entangled coherent states is proposed.

Electron Entanglement Detected by Quantum Spin Hall Systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.

Using macroscopic entanglement to close the detection loophole in Bell-inequality tests

We consider a Bell-like inequality performed using various instances of multi-photon entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the "size" of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more "macroscopic" form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loophole. Differently, losses before the unitary transformations cause decoherence effects that cannot be compensated using macroscroscopic entanglement.

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.

Bell-inequality tests with entanglement between an atom and a coherent state in a cavity

We study Bell-inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on-off measurements and photon number parity measurements, respectively, are investigated. When photon on-off measurements are used, at least 50$%$ of detection efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son's bound. We also analyze decoherence effects in both field and atomic modes and discuss conditions required to perform a Bell inequality test free from the locality loophole.

Bell-inequality tests with macroscopic entangled states of light

Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole and the locality loophole simultaneously is highly desirable and remains challenging. A novel approach to a loophole-free Bell tests is based on amplification of the entangled photons, i.e.\@ on macroscopic entanglement, which optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by the classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell test and quantum protocols are the subject of an intensive study in the field nowadays.

Bell inequality for pairs of particle-number-superselection-rule restricted states

Proposals for Bell-inequality tests on systems restricted by the particle-number-superselection rule often require operations that are difficult to implement in practice. In this article, we derive a Bell inequality, where measurements on pairs of states are used as a method to bypass this superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in an identical pair of states when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.

Bell inequality tests of four-photon six-qubit graph states

We report on the experimental realization of two different Bell inequality tests based on six-qubit linear-type and Y-shape graph states. For each of these states, the Bell inequalities tested are optimal in the sense that they provide the maximum violation among all Bell inequalities with stabilizing observables and possess the maximum resistance to noise.

Testing Bell inequality at experiments of high energy physics

Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal raised in literature and use the successive decays J/ψ → γηc → Λλ̄ → pπ−p̄π+ to testify the Bell inequality. Our goal is twofold, namely, we first make a Monte–Carlo simulation of the processes based on the quantum field theory (QFT). Since the underlying theory is QFT, it implies that we pre-admit the validity of quantum picture. Even though the QFT is true, we need to find how big the database should be, so that we can clearly show deviations of the correlation from the Bell inequality determined by the local hidden variable theory. There have been some critiques on the proposed method, so in the second part, we suggest some improvements which may help to remedy the ambiguities indicated by the critiques. It may be realized at an updated facility of high energy physics, such as BES III.

Effects of squeezing on quantum nonlocality of superpositions of coherent states

We analyze effects of squeezing upon superpositions of coherent states (SCSs) and entangled coherent states (ECSs) for Bell-inequality tests. We find that external squeezing can always increase the degrees of Bell violations, if the squeezing direction is properly chosen, for the case of photon parity measurements. On the other hand, when photon on/off measurements are used, the squeezing operation can enhance the degree of Bell violations only for moderate values of amplitudes and squeezing. We point out that a significant improvement is required over currently available squeezed SCSs in order to directly demonstrate a Bell-inequality violation in a real experiment.