Linear Program for Testing Nonclassicality and an Open-Source Implementation.

A well-motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex embeddability as introduced in Schmid et al. [PRX Quantum 2, 010331 (2021).2691-339910.1103/PRXQuantum.2.010331] and generalized in Selby et al. [Phys. Rev. A 107, 062203 (2023).PLRAAN2469-992610.1103/PhysRevA.107.062203].

Revisiting Dynamics of Quantum Causal Structures-When Can Causal Order Evolve?

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Castro-Ruiz et al. pursues this using the process-matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Our result here challenges that of Castro-Ruiz et al.: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then the conclusion of Castro-Ruiz et al. does not hold. That is, we show that under certain continuous and reversible dynamics, the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on physical dynamics. Finally, we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.

Contextuality without Incompatibility.

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

Bipartite Postquantum Steering in Generalized Scenarios.

The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the "instrumental steering" scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.

Reference Frames Which Separately Store Noncommuting Conserved Quantities.

Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a "battery" for a distinct quantity. For systems composed of spin-1/2 particles, we show that the components of angular momentum S_{x}, S_{y}, and S_{z} (noncommuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of noncommuting conserved quantities.

Almost-Quantum Correlations Violate the No-Restriction Hypothesis.

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost-quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalized probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost-quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost-quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other nonsignaling ones.

Quantum reference frames and their applications to thermodynamics.

We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Postquantum Steering.

The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While post-quantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.