Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognized as a consequence of the exclusivity principle(EP). We provide an operational criterion for monogamy: if the fractional packing number of the graph corresponding to the union of event sets of several physical experiments does not exceed the sum of independence numbers of each individual experiment graph, then these experiments are monogamous. As applications of this observation, several examples are provided, including the monogamy for experiments of Clauser-Horne-Shimony-Holt (CHSH) type, Klyachko-Can-Binicioğlu-Shumovsky (KCBS) type, and for the first time, we give some monogamy relations of Svetlichny's genuine nonlocality. We also give the necessary and sufficient conditions for several experiments to be monogamous: several experiments are monogamous if and only if the Lovász number of the union exclusive graph is less than or equal to the sum of independence numbers of each exclusive graph.
We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.
It is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature, based on quantum mechanics. One possible explanation is the "global exclusivity" principle recently discussed in Phys. Rev. Lett. 110, 060402 (2013). In this work we show that this principle actually has a much stronger restriction on the probability distribution. We provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph. Our result implies that the exclus…
The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the Exclusivity principle singles out the maximum quantum value for some important Bell and noncontextuality inequalities. We can get better results if we apply the E principle to more sophisticated scenarios. This happens because this principle exhibits activation effects: a distribution satisfying this principles does not necessarily satisfy it when combined with…
We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for …
A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We char…
The question concerning the physical realizability of a probability distribution is of quite importance in Quantum foundations. Specker first pointed out that this question cannot be answered from Kolmogorov's axioms alone. Lately, this observation of Specker has motivated simple principles (exclusivity principle/ local orthogonality principle) that can explain quantum limit regarding the possible sets of experimental probabilities in various nonlocality and contextuality experiments. We study Specker's observation in the simplest scenario involving three inputs each with two outputs. Then usi…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and update them when new information becomes available. Our framework includes as special cases classical and quantum probability theory, as well as other forms of probabilistic reasoning that may arise in future physical theories. Building on this framework, we develop a notion of ideal experiment, which in quantum theory coincides with the notion of projective …
We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum non-locality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.
In this paper we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no-disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs …
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure $A$ simultaneously with $B$, another to measure $B$ with $C$, and another to measure $A$ with $C$, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, sur…
Physical principles constraints the way nonlocal correlations can be distributed among distant parties in a Bell-type experiment. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed by a set of parties by the violation observed by a different set of parties. Here we show that the no-signaling principle yields a simple and tight monogamy relations for an important class of bipartite and multipartite Bell inequalities. We also link these trade-offs to the guessing probability--a key quantity in the device-independent informati…
In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this a…
We show that the no-disturbance principle imposes a tradeoff between locally contextual correlations violating the Klyachko-Can-Binicioglu-Shumovski inequality and spatially separated correlations violating the Clauser-Horne-Shimony-Holt inequality. The violation of one inequality forbids the violation of the other. We also obtain the corresponding monogamy relation imposed by quantum theory for a qutrit-qubit system. Our results show the existence of fundamental monogamy relations between contextuality and nonlocality that suggest that entanglement might be a particular form of a more fundame…
Physical principles constrain the way nonlocal correlations can be distributed among distant parties. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed among a set of parties by the violation observed by a different set of parties. We prove here that much stronger monogamy relations are possible for nonsignalling correlations by showing how nonlocal correlations among a set of parties limit any form of correlations, not necessarily nonlocal, shared among other parties. In particular, we provide tight bounds between the vio…
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem that remains open, and one approach to explaining its origins is the so-called Exclusivity principle, relying on probabilistic assumptions shaping general probabilistic theories through sharp measurements and compatible (non-local) measurements. Information indistinguishability, presented here as indistinguishability of qubits and more general bits, may serve as an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. We connect indistinguishability to the…
Non-contextuality (NC) and Bell inequalities can be expressed as bounds $Ω$ for positive linear combinations $S$ of probabilities of events, $S \leq Ω$. Exclusive events in $S$ can be represented as adjacent vertices of a graph called the exclusivity graph of $S$. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel-Lovász-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing $S$ over the…
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entro…
Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (https://vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations.…
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the …
Quantum $n$-body correlations cannot be explained with $(n-1)$-body nonlocality. However, this genuine $n$-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any $n \ge 2$, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and $n$-body nonlocality, and connects two programs towards understanding quantum theory.
