Quantum nonlocality can be observed in networks even in the case where every party can only perform a single measurement, i.e. does not receive any input. So far, this effect has been demonstrated under the assumption that all sources in the network are fully independent from each other. Here we investigate to what extent this independence assumption can be relaxed. After formalizing the question, we show that, in the triangle network without inputs, quantum nonlocality can be observed, even when assuming only an arbitrarily small level of independence between the sources. This means that quantum predictions cannot be reproduced by a local model unless the three sources can be perfectly correlated.
The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest Bell test - one involving 2 parties each performing 2 binary-outcome measurements - an arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality. To this end, we introduce the notion of measurement dependent locality and show that the corresponding correlations form a convex polytope. These correlations can thus be char…
Bell's theorem asserts that no model that satisfies all of the plausible physical assumptions of outcome independence (OI), measurement independence (MI) and Parameter Independence (PI) can reproduce quantum mechanics. Here I find the optimum model that saturates CHSH inequality for the case that outcome independence and measurement independence hold but parameter dependence is allowed. I find the bound as a function of a measure of parameter dependence and show that the model proposed by [New Journal of Physics,12(8):083051] is optimal for one-way parameter dependence. The symbolic optimizati…
Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural assumptions of no-signaling and independence of the sources. We consider the ``triangle network'', and derive strong constraints on correlations even though the parties receive no input, i.e. each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variabl…
If Nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here it is shown that generalized uncertainty relations, as well as a specific notion of locality give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which …
In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the hidden variables do not in any way depend on measurement settings" and that, consequently, the experimental violations of Bell inequalities "show that maintaining local causality requires violating statistical independence". However, Hance and Hossenfelder also argue that "we should (...) look for independent experimental evidence that can distinguish the two d…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We study the case where this assumption is weakened, so that measurement settings and local variables are at least partially correlated. As we show, there is a connection between this type of model and models which reproduce nonlocal correlations by allowing classical communication between the distant parties, and a connection with models…
The correlations between three arbitrarily far-apart regions of the vacuum state of the free Klein-Gordon field are investigated by means of its finite duration coupling to three localized detectors. It is shown that these correlations cannot be reproduced in terms of a hybrid local-nonlocal hidden-variable model, i.e., the correlations between three arbitrarily separated regions of the vacuum are fully nonlocal.
We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al, Nature Physics 2012], we show that any combination of local common causes and direct causes satisfying this principle, i.e. propagating at any finite speed, leads to signalling. This is true even if the common and direct causes are allowed to propagate at a supraluminal-but-finite speed defined in a Newtonian-like privileged universal reference frame. Consequ…
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.…
It has previously been shown that quantum nonlocality offers no benefit over classical correlations for performing a distributed task known as nonlocal computation. This is where separated parties must compute the value of a function without individually learning anything about the inputs. We show that giving the parties some knowledge of the inputs, however small, is sufficient to unlock the power of quantum mechanics to out-perform classical mechanics. This role of information held locally gives new insight into the general question of when quantum nonlocality gives an advantage over classic…
We show that it is possible to have arbitrarily long sequences of Alices and Bobs so every (Alice, Bob) pair violates a Bell inequality. We propose an experiment to observe this effect with two Alices and two Bobs.
Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit 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) Bell inequality with the single Alice. This scenario was introduced in [Phys. Rev. Lett. 114, 250401 (2015)] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evi…
In Phys. Rev. Lett. \textbf{104},170401 (2010), Branciard \textit{e.t al.} first characterized the correlations arising in an entanglement swapping network under the assumption that the sources generating the initially uncorrelated quantum systems are independent. Precisely speaking, in Phys. Rev. Lett. \textbf{104},170401 (2010) and later in Phys. Rev. A \textbf{85},032119 (2012) the authors analyzed the importance of \textit{bilocal}(source independence) assumption to lower down the restrictions over correlations for revealing quantumness in the network where each of two sources generates a …
Almost all pure entangled states enable unbounded nonlocality sharing
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学与技术研究院）；Physics Department and NanoLund, Lund University（隆德大学物理系与纳米实验室）
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner [Nat. Commun. 2, 411 (2011)], we then show that any nontrivial account of these correlations in the form of an extension…
Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light…
Device independent protocols based on Bell nonlocality, such as quantum key distribution and randomness generation, must ensure no adversary can have prior knowledge of the measurement outcomes. This requires a measurement independence assumption: that the choice of measurement is uncorrelated with any other underlying variables that influence the measurement outcomes. Conversely, relaxing measurement independence allows for a fully `causal' simulation of Bell nonlocality. We construct the most efficient such simulation, as measured by the mutual information between the underlying variables an…
Quantum nonlocality stands as a resource for Device Independent Quantum Information Processing (DIQIP), as, for instance, Device Independent Quantum Key Distribution. We investigate experimentally the assumption of limited Measurement Dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [Phys. Rev. Lett. 113 190402] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the ine…
Bell's theorem is purported to demonstrate the impossibility of a local "hidden variable" theory underpinning quantum mechanics. It relies on the well-known assumption of `locality', and also on a little-examined assumption called `statistical independence' (SI). Violations of this assumption have variously been thought to suggest "backward causation", a "conspiracy" on the part of nature, or the denial of "free will". It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories…
We address the problem of detecting bipartite Bell nonlocality whenever the only experimental information are the intensities produced in each run of the experiment by an unknown number of particles. We point out that this scenario naturally occurs in Bell experiments with parametric down-conversion when the crystal is pumped by strong pulses, in Bell tests with distant sources and in which particles suffer different delays during their flight, in Bell experiments using living cells as photo detectors, and in Bell experiments where the pairing information is physically removed. We show that, a…
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many …
In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from cau…
The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with non-detection events due to losses and detector inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, e.g. in each run of the experiment the overall detection efficiency is lower bounded by $η_{min} > 0$. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control ove…
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model, called a violation of measurement independence, would mean a violation of experimenters freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thu…
We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and quantum algorithm, implying nonlocal attacks of noise. We then argue that the quantum error correction method fails to protect quantum computation against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This shows that the implicit assumption of quantum error correction theory -- independence of noise and self-dynamics -- fails in long time regime…
There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L…
Sequential quantum nonlocality sharing under local noisy quantum channels
Hebei Normal University（河北师范大学）；Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所）；Shijiazhuang Posts and Telecommunications Technical College（石家庄邮电职业技术学院）；University of Chinese Academy of Sciences（中国科学院大学）
We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding 'one-sided monogamy relations' that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum…
The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with non-detection events due to losses and detectors' inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by $η_{min} > 0$. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full cont…
Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work by M.O.Renou, et al., in [1], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In [1], the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios is yet to be…
We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also ob…
All pure entangled states can lead to fully nonlocal correlations
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学与技术学院）；Laboratoire d’Information Quantique, Université libre de Bruxelles (ULB)（布鲁塞尔自由大学量子信息实验室）；Center for Quantum-Enabled Computing, Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心量子计算中心）；ICREA - Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚高级研究协会）
Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science which was confirmed in the experiments proving the violation of Bell Inequalities (BI). It has been known already for a long time that the probabilistic models used to prove BI for spin polarization correlation experiments (SPCE) are incompatible with the experimental protocols of SPCE. In particular these models use a common probability space together with joint probability distributions for various incompatible coincidence experiments and/or conditional independence (Bell's local…
Bell nonlocality between distant quantum systems---i.e., joint correlations which violate a Bell inequality---can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell nonlocality requires high detection efficiencies, and is not robust to the typical transmission losses that occur in long distance applications. In contrast, quantum steering, a weaker form of quantum correlation, can be verified fo…
A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the measurement, via some common cause. Hence, to derive no-go results such as Bell inequalities, an assumption of measurement independence is crucial. It is a surprisingly strong assumption -- less than 1/15 bits of prior correlation suffice for a local model of the singlet state of two qubits -- with ramifications for the security of quantum communi…
The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it…
