Local quantum measurement and no-signaling imply quantum correlations

Principle of Information Causality Rationalizes Quantum Composition

The principle of information causality, proposed as a generalization of no signaling principle, has efficiently been applied to outcast beyond quantum correlations as unphysical. In this Letter, we show that this principle, when utilized properly, can provide physical rationale toward structural derivation of multipartite quantum systems. In accordance with the no signaling condition, the state and effect spaces of a composite system can allow different possible mathematical descriptions, even when descriptions for the individual systems are assumed to be quantum. While in one extreme, namely, the maximal tensor product composition, the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, the other extreme-minimal tensor product composition-contains only separable states, and the resulting theory allows only Bell local correlation. As we show, none of these compositions is commensurate with information causality, and hence cannot be the bona-fide description of nature. Information causality therefore promises an information-theoretical derivation of self duality of the state and effect cones for composite quantum systems.

Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm

Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive a mathematical formulation of the theory by identifying the general structure of state and effect space of individual systems as well as specifying their composition rules. This generic framework can allow several consistent composition rules for a multipartite system even when state and effect cones of individual subsystems are assumed to be quantum. Nevertheless, for any bipartite system, none of these compositions allows beyond quantum spacelike correlations. In this Letter, we show that such bipartite compositions can admit stronger-than-quantum correlations in the timelike domain and, hence, indicates pragmatically distinct roles carried out by state and effect cones. We discuss consequences of such correlations in a communication task, which accordingly opens up a possibility of testing the actual composition between elementary quanta.

An information-theoretic principle implies that any discrete physical theory is classical

It has been suggested that nature could be discrete in the sense that the underlying state space of a physical system has only a finite number of pure states. Here we present a strong physical argument for the quantum theoretical property that every state space has infinitely many pure states. We propose a simple physical postulate that dictates that the only possible discrete theory is classical theory. More specifically, we postulate that no information gain implies no disturbance or, read in the contrapositive, that disturbance leads to some form of information gain. Furthermore, we show that non-classical discrete theories are still ruled out even if we relax the postulate to hold only approximately in the sense that no information gain only causes a small amount of disturbance. Our postulate also rules out popular generalizations such as the Popescu-Rohrlich-box that allows non-local correlations beyond the limits of quantum theory.

A violation of the uncertainty principle implies a violation of the second law of thermodynamics

Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? Here we give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.

Quantum correlations with no causal order

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? Here, we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.

Causal order is a concept that is engrained in the standard understanding of time, both in classical and quantum mechanics. Oreshkov et al. generalize the standard formalism of quantum theory to a framework with no pre-existing causal order, and find a new class of correlations that have no analogue in the classical world.

Typical local measurements in generalized probabilistic theories: emergence of quantum bipartite correlations

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

Deriving quantum theory from its local structure and reversibility

We investigate the class of physical theories with the same local structure as quantum theory but potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory can be simulated in quantum theory but that this does not hold for tripartite correlations. Here we explore whether imposing an additional constraint on this space of theories-that of dynamical reversibility-will allow us to recover the global quantum structure. In the particular case in which the local systems are identical qubits, we show that any theory admitting at least one continuous reversible interaction must be identical to quantum theory.

Structure of reversible computation determines the self-duality of quantum theory

Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors--quantum theory is self-dual. In this Letter, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logical bit can be mapped to any other logical bit by a reversible transformation. Specifically, we consider probabilistic theories more general than quantum theory, and prove that every bit-symmetric theory must necessarily be self-dual. We also show that bit symmetry yields stronger restrictions on the set of allowed bipartite states than the no-signalling principle alone, suggesting reversible time evolution as a possible reason for limitations of nonlocality.

Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system

Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property can be singled out using graph theory. Here we report the experimental observation of an impossible-to-beat quantum advantage on a four-dimensional quantum system defined by the polarization and orbital angular momentum of a single photon. The results show pristine evidence of the quantum advantage and are compatible with the maximum advantage allowed using postquantum resources.

No-signaling principle can determine optimal quantum state discrimination

We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the no-signaling principle. This is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication. Finally, a general bound to the guessing probability is presented in a closed form.

Bell inequalities with no quantum violation and unextendable product bases

The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality-displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases with a wide family of tasks, for which (i) quantum correlations do not outperform the classical ones but (ii) there exist supraquantum nonsignaling correlations that do provide an advantage.

The uncertainty principle determines the nonlocality of quantum mechanics

Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.