Bell Inequality Violation Research Articles

Violating Bell inequalities with entangled optical frequency combs and multipixel homodyne detection

We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities - for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements - in a multi-party configuration where each participant is given a section, in the frequency domain, of the output of an optical parametric oscillator which has been synchronously-pumped with a frequency comb. Such light sources are undergoing intense study due to their novel properties, including the potential for production of light entangled in many hundreds of physical modes - a critical component for many proposals in optical or hybrid-optical quantum computation proposals. The situation we study notably uses only highly-efficient optical homodyne detection, meaning that in such systems the fair-sampling loophole would be relatively easy to avoid.

Response in the violation of the Bell inequality to imperfect photon addition and subtraction in noisy squeezed states of light

Violation of Bell inequality is a prominent detection method for quantum correlations present in composite quantum systems, both in finite and infinite dimensions. We investigate the consequence of the violation of local realism based on pseduospin operators when photons are added or subtracted in a single mode or in both the modes of the two-mode squeezed states of light in the presence of noise. In the noiseless situation, we show that for addition (subtraction) of photons in a single mode, there is an overall enhancement in the maximal violation, although we observe an interplay between monotonicity and nonmonotonicity in the violation of Bell inequality depending on the squeezing strength. Moreover, we report that for low squeezing or low number of photons added or subtracted, subtraction in both the modes can lead to higher violation of local realism than that in the case of addition. For any choice of parameters, such ordering is not seen if one compares their entanglement contents. In the event of a faulty twin-beam generator, we obtain a lower than expected squeezing in the state. In such a case, or in imperfect photon addition (subtraction) or under local noise, we find that the violation of local realism by the noise-affected two-mode squeezed states always decreases. Interestingly, however, we notice that photon addition (subtraction) can in general help to conquer the ill effects of noise by enhancing the violation of local realism or by transforming nonviolating states to violating ones, thereby acting as an activating agent.

Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations.

We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.

An Ontology of Nature with Local Causality, Parallel Lives, and Many Relative Worlds

Parallel Lives (PL) is an ontological model of nature in which quantum mechanics and special relativity are unified in a single universe with a single space-time. Point-like objects called lives are the only fundamental objects in this space-time, and they propagate at or below c, and interact with one another only locally at point-like events in space-time, very much like classical point particles. The only causes and effects in the universe occur when lives meet locally, and thus the causal structure of interaction events in space-time is Lorentz invariant. Each life traces a continuous world-line through space-time, and experiences its own relative world, fully defined by the outcomes of past events along its world-line (never superpositions), which are encoded in its external memory. A quantum field comprises a continuum of lives throughout space-time, and familiar physical systems like particles each comprise a sub-continuum of the lives of the field. Each life carries an internal memory containing a local relative wavefunction, which is a local piece of a pure universal wavefunction, but only the relative wavefunctions are physically real in PL, and not the universal wavefunction in configuration space. Furthermore, while the universal wavefunction tracks the average behavior of the lives of a system, it fails to track their individual dynamics and trajectories. There is always a preferred separable basis, and for an irreducible physical system, each orthogonal term in this basis is a different relative world - each containing some fraction of the lives of the system. The relative wavefunctions in the lives' internal memories govern which lives of different systems can meet during future local interactions, and thereby enforce entanglement correlations - including Bell inequality violations.

Bell inequalities violation within non-Bunch–Davies states

In this Letter, we study the quantum nature of non-Bunch–Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons–Hawking temperature, the CHSH bound degrades monotonously for Bunch–Davies vacuum sector. Due to the intrinsic correlation of non-Bunch–Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch–Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell's Theorem.

Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission, and measurement of a single quantum system, in other words, quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realize such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the postquantum Bell correlations obeying only locality in the macroscopic limit. We find that the advantages are tied to the use of measurements that are not rank-one projective, and provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.

Extended Bell inequality and maximum violation**Project supported in part by the National Natural Science Foundation of China (Grant Nos. 11275118 and U1330201).

The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the BI, while the violation is a direct result of the non-local quantum interference between two components of entangled state. The Bell measuring outcome correlation denoted by PB is always less than or at most equal to one for the local realistic model () regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as , which, however depends on state parameters and three measuring directions as well. Our result is suitable for entangled photon pairs.

Device-independent quantum random-number generation.

Randomness is important for many information processing applications, including numerical modelling and cryptography1,2. Device-independent quantum random-number generation (DIQRNG)3,4 based on the loophole-free violation of a Bell inequality produces genuine, unpredictable randomness without requiring any assumptions about the inner workings of the devices, and is therefore an ultimate goal in the field of quantum information science5-7. Previously reported experimental demonstrations of DIQRNG8,9 were not provably secure against the most general adversaries or did not close the 'locality' loophole of the Bell test. Here we present DIQRNG that is secure against quantum and classical adversaries10-12. We use state-of-the-art quantum optical technology to create, modulate and detect entangled photon pairs, achieving an efficiencyof more than 78 per cent from creation to detection at a distance of about 200 metres that greatly exceeds the threshold for closing the 'detection' loophole of the Bell test. By independently and randomly choosing the base settings for measuring the entangled photon pairs and by ensuring space-like separation between the measurement events, we also satisfy the no-signalling condition and close the 'locality' loophole of the Bell test, thus enabling the realization of the loophole-free violation of a Bell inequality. This, along with a high-voltage, high-repetition-rate Pockels cell modulation set-up, allows us to accumulate sufficient data in the experimental time to extract genuine quantum randomness that is secure against the most general adversaries. By applying a large (137.90 gigabits×62.469 megabits) Toeplitz-matrix hashing technique, we obtain 6.2469×107 quantum-certified random bits in 96 hours with a total failure probability (of producing a random number that is not guaranteed to be perfectly secure) of less than 10-5. Our demonstration is a crucial step towards transforming DIQRNG from a concept to a key aspect of practical applications that require high levels of security and thus genuine randomness7. Our work may also help to improve our understanding ofthe origin of randomness from a fundamental perspective.

Optimal quantum preparation contextuality in an n -bit parity-oblivious multiplexing task

In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum preparation contextuality can power the parity-oblivious multiplexing (POM) task. The bound on the optimal success probability of $n$-bit POM task performed with the classical resources was shown to be the \textit{same} as in a preparation non-contextual theory. This non-contextual bound is violated if the task is performed with quantum resources. While in $2$-bit POM task the optimal quantum success probability is achieved, in 3-bit case optimality was left as an open question. In this paper, we show that the quantum success probability of a $n$-bit POM task is solely dependent on a suitable $2^{n-1}\times n$ Bell's inequality and optimal violation of it optimizes the success probability of the said POM task. Further, we discuss how the degree of quantum preparation contextuality restricts the amount of quantum violations of Bell's inequalities, and consequently the success probability of a POM task.

Test for a large amount of entanglement, using few measurements

Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement,nEPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubiti, and the other is told to play games on qubits{i,j}, without knowing which index isi.The test is robust: a success probability withinδof optimal guarantees distanceO(n5/2δ)fromnEPR states. However, the test does not tolerate constantδ; it breaks down forδ=Ω~(1/n). We give an adversarial strategy that succeeds within delta of the optimum probability using onlyO~(δ−2)EPR states.

Trade-offs in multiparty Bell-inequality violations in qubit networks

Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.

Multi-time quantum correlations with no spatial analog

Multipartite quantum correlations are a powerful resource that underpins applications from quantum metrology to quantum computing. While most research has focused on spatial correlations, it is now becoming clear that a sequence of measurements on a single quantum system at different points in time reveals a similarly rich, yet fundamentally different structure of multipartite temporal correlations. Here we experimentally observe genuine multi-time correlations in a sequence of three generalized measurements on a single photon. These correlations, manifest by a simultaneous violation of all pairwise Bell inequalities, cannot be reproduced by any spatial quantum state of equal dimension. Our work lays the foundation for the exploration of temporal correlations arising in quantum networks for quantum information applications.

Robust Bell inequalities from communication complexity

The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say that a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given for the quantum violation of these Bell inequalities in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. This makes the Bell inequality resistant to the detection loophole, while a normalized Bell inequality is resistant to general local noise. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bound techniques. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.

Simulability of observables in general probabilistic theories

The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A scheme for obtaining new observables from existing ones via classical operations, the so-called simulation of observables, has led to an extension of the notion of compatibility for measurements. We consider the simulation of observables within the operational framework of general probabilistic theories and introduce the concept of simulation irreducibility. While a simulation irreducible observable can only be simulated by itself, we show that any observable can be simulated by simulation irreducible observables, which in the quantum case correspond to extreme rank-1 positive-operator-valued measures. We also consider cases where the set of simulators is restricted in one of two ways: in terms of either the number of simulating observables or their number of outcomes. The former is seen to be closely connected to compatibility and $k$-compatibility, whereas the latter leads to a partial characterization for dichotomic observables. In addition to the quantum case, we further demonstrate these concepts in state spaces described by regular polygons.

Towards Experiments to Test Violation of the Original Bell Inequality.

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser–Horne–Shimony–Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein–Podolsky–Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR–Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound to the classical bound i.e., is less than the fraction of the quantum bound for the OB inequality to the classical bound i.e., Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.

Classical Causal Models for Bell and Kochen-Specker Inequality Violations Require Fine-Tuning

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.

Classical versus quantum communication in XOR games

We introduce an intermediate setting between quantum nonlocality and communication complexity problems. More precisely, we study the value of XOR games when Alice and Bob are allowed to use a limited amount (c bits) of one-way classical communication compared to their value when they are allowed to use the same amount of one-way quantum communication (c qubits). The key quantity here is the ratio between the quantum and classical value. We provide a universal way to obtain Bell inequality violations of general Bell functionals from XOR games for which the previous quotient is larger than 1. This allows, in particular, to find (unbounded) Bell inequality violations from communication complexity problems in the same spirit as the recent work by Buhrman et al. (PNAS 113(12):3191–3196, 2016). We also provide an example of a XOR game for which the previous quotient is optimal (up to a logarithmic factor) in terms of the amount of information c. Interestingly, this game has only polynomially many inputs per player. For the related problem of separating the classical versus quantum communication complexity of a function, the known examples attaining exponential separation require exponentially many inputs per party.

Experimentally generated randomness certified by the impossibility of superluminal signals.

From dice to modern electroniccircuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable1-3. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity1-11. With recent technological developments, it is now possible to carry out such a loophole-free Bell test12-14,22. Here we present certified randomness obtained from a photonic Bell experiment and extract 1,024 random bits that are uniformly distributed to within 10-12. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.

Experimental verification of a new Bell-type inequality

Arpan Das et al. proposed a set of new Bell inequalities (Das et al., 2017 [16]) for a three-qubit system and claimed that each inequality within this set is violated by all generalized Greenberger–Horne–Zeilinger (GGHZ) states. We investigate experimentally the new inequalities in the three-photon GGHZ class states. Since the inequalities are symmetric under the identical particles system, we chose one Bell-type inequality from the set arbitrarily. The experimental data well verified the theoretical prediction. Moreover, the experimental results show that the amount of violation of the new Bell inequality against locality realism increases monotonically following the increase of the tangle of the GGHZ state. The most profound physical essence revealed by the results is that the nonlocality of GGHZ state correlate with three tangles directly.

Fidelity deviation in quantum teleportation

We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.