Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe real states of the real While Bell inequalities put into question the reality of states, modern device-independent approaches do away with the idea of entities: physics is not built of physical systems. Focusing on the correlations between operationally defined inputs and outputs, device-independent methods promote a view more distant from conventional theory than Einstein's 'principle theories' were from 'constructive theories'. On the examples of indefinite causal orders and almost quantum correlations, we ask a puzzling question: if physical theory is not about systems, then what is it about? The answer given by the device-independent models is that physics is about languages. In moving away from the information-theoretic reconstructions of quantum theory, this answer marks a new conceptual development in the foundations of physics.
Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe real states of the real While Bell inequalities put into question the reality of states, modern device-independent approaches do away with the idea of entities: physics is not built of physical systems. Focusing on the correlations between operationally defined inputs and outputs, device-independent methods promote a view more distant from conventional theory than Einstein's 'principle theories' were from 'constructive theories'. On the examples of indefinite causal orders and almost quantum correlations, we ask a puzzling question: if physical theory is not about systems, then what is it about? The answer given by the device-independent models is that physics is about languages. In moving away from the information-theoretic reconstructions of quantum theory, this answer marks a new conceptual development in the foundations of physics.
The Einstein–Podolsky–Rosen paradox and Bell’s theorem sit at the center of one of the most famous unresolved questions in physics: how can distant quantum outcomes remain so perfectly correlated without reducing reality to either hidden variables or some troubling form of nonlocality? For nearly a century, this debate has shaped the foundations of quantum theory, the interpretation of entanglement, and, more recently, the conceptual language surrounding quantum information and quantum computing. Yet one possibility may still be underexplored: what if the puzzle begins from the wrong ontological starting point? This paper asks exactly that question. Standard quantum mechanics already accepts many systems as physically unified wholes described by a single composite wavefunction: atoms, multi-electron states, molecular orbitals, and hadrons. Even increasingly large molecules continue to exhibit interference, showing that quantum oneness is not destroyed simply by size or spatial extension. If such preserved composite oneness is already an accepted part of quantum theory, then why is the EPR–Bell pair so often framed first as two independently sufficient distant objects? The proposal developed here is both simple and provocative: the EPR–Bell pair may, prior to measurement, belong to the same ontological class as other accepted composite quantum systems. On this view, the pair is not first two complete distant realities that must somehow remain coordinated across space, but one preserved composite wavefunction whose support spans separated regions and whose distinct local outcomes emerge only when the whole state is resolved. If that is right, then one of the deepest questions in modern physics changes form. The issue is no longer simply how two distant objects stay correlated. The issue becomes whether the assumption of separability was imposed too early. This paper develops that conjecture step by step, using accepted quantum examples, the original EPR question, Bell’s constraint, and the logic of composite Wavefunction Oneness. The result is a new way of reopening the nonlocality problem—not by denying Bell, and not by proposing hidden variables, but by asking whether the EPR–Bell discussion has been starting from the wrong picture of what the physical system actually is.
For over a century, we have sought to understand the abstract formulation of quantum theory from more convincing physical arguments, and this is one of the most enticing scientific challenges of recent times: to derive quantum theory from simple physical principles. There are various ideas on how to approach this, and at least two different approaches to the problem stand out. The first consists of assuming general probabilistic theories that allow probability distributions more general than those that arise in quantum theory, with the goal of finding principles that select quantum theory from this range of possible theories, reconstructing quantum theory as a purely operational probabilistic theory that follows from certain sets of axioms. Although successful, this approach does not completely resolve the problem. Another approach goes in a different direction. Instead of attempting to reconstruct quantum theory as a whole, the focus is on understanding which physical principles explain two of the most peculiar aspects of quantum theory: nonlocality and contextuality, using a device-independent approach. This is one of the key questions we aim to investigate with this masters project: what are the physical principles that explain nonlocality and contextuality in quantum systems?
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in non-relativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, in a physical system such as an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.
Bell scenarios are multipartite scenarios that exclude any signalling between parties. This leads to a strict hierarchy of classical, quantum, and non-signalling correlations in such scenarios. Here we consider a minimal relaxation of non-signalling: each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. Crucially, unlike Bell, we make no global assumption about causal relations between parties, e.g., they could be embedded in some exotic spacetime with indefinite causal order. We do make a causal assumption local to each party, i.e., the input received by it causally precedes the output it sends out. We then ask: Can we device-independently certify the nonclassicality of multipartite correlations in such scenarios, just as Bell inequality violations do so in Bell scenarios? A priori, this is not clear: without some assumptions on the underlying physics (e.g., non-signalling), parties can realize arbitrary correlations. We therefore make a minimal assumption of logical consistency on the underlying physics, i.e., it must be free of time-travel antinomies without imposing any restrictions on local interventions of the parties. We then define antinomicity as a device-independent notion of nonclassicality and prove a strict hierarchy between correlation sets based on their antinomicity. An antinomic correlation cannot be explained by a classical physical theory compatible with free local interventions on pain of logical contradictions in the theory. On the other hand, parties exchanging quantum systems can witness antinomicity while respecting logical consistency. Antinomicity reduces to Bell nonlocality for non-signalling parties. It also resolves a conceptual puzzle, namely, the failure of causal inequalities as witnesses of nonclassicality: antinomicity implies causal inequality violations, but not conversely.
Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in nonrelativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave, or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. It is not an element of physics. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, for an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.