41 pages. Greatly extended version of quant-ph/0304159 with several additional topics discussed--more philosophical material toward the beginning, more technical (but still fairly discursive) material toward the end
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical theory, and more. Whatever else they may be, quantum states of systems are compendia of probabilities for the outcomes of possible operations we may perform on the systems: ``operational theories.'' I discuss appropriate general frameworks for such theories, in which convexity plays a key role. Such frameworks are appropriate for investigating what things look like from an ``inside view,'' i.e. for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ``geometric'' picture (``outside view'') coordinating them all can be had, even if this picture is very different in nature from the structure of the perspectives within it, is the key to understanding whether we may be able to achieve a unified, ``objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ``geometric'' conception of physics. The nature of information, its flow and processing, as seen from various operational persepectives, is likely to be key to understanding whether and how such coordination and unification can be achieved.
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary role among several stunning features of quantum theory. The purpose of this thesis is to investigate fundamental aspects of uncertainty. In particular, we address this problem focusing on convexity, which has an operational origin. We first try to reveal why in quantum theory similar bounds are often obtained for two types of uncertainty relations, namely, …
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand side of uncertainty relation is generally not operational as it depends on the quantum formalism. Also, while joint non-measurability of observables is an operational notion, the complementarity in Bohr sense (i.e. excess of information needed to describe the system) has not yet been expressed in purely operational terms. In this paper we propose a solution…
Brussels Free University（布鲁塞尔自由大学）；Laboratorio di Autoricerca di Base（基础自主研究实验室）；School of Management and Institute IQSCS（管理学院与IQSCS研究所）
The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approaches to the foundations of quantum physics. The deep analogies between the foundations of physics and cognition lead us to investigate the validity of quantum theory as a general and unitary framework …
An elucidation of the current state of art in quasi-Hermitian quantum theory (QHQT) as inspired by the recent paper by Alase et al (J. Phys. A: Math. Theor. 55 (2022) 244003, paper [1]) is offered. We point out that the author's main discovery (viz., that the QHQT does not extend the standard quantum theory) is not new. In a related comment on the author's method of proof performed in ``the framework of general probabilistic theories'' (GPT) we add that also in this context a few other, mathematically consistent GPT-like theories are already available in the literature (pars pro toto we mentio…
We undertake a reconstruction of the epistemic significance of research on operational theories in quantum foundations. We suggest that the space of operational theories is analogous to the space of possible worlds employed in the possible world semantics for modal logic, so research of this sort can be understood as probing modal structure. Thus we argue that operational axiomatisations of quantum mechanics may be interpreted as a novel form of structural realism; we discuss the consequences of this interpretation for the philosophy of structural realism and the future of operational theories…
An operational concept of locality whose quantum violation is indicated independently of any other assumption(s) seems to be lacking in the quantum foundations literature so far. Bell's theorem only shows that quantum correlations violate the conjunction of the ontological assumptions of localism and determinism. Taking a cue from computational complexity theory, here we define such a concept of locality in terms of a class of operational decision problems, and propose that Einstein-Podolsky-Rosen (EPR) steering in its basic asymmetric formulation gives a specific realization of this class. Va…
We discuss a novel framework for physical theories that is based on the principles of locality and operationalism. It generalizes and unifies previous frameworks, including the standard formulation of quantum theory, the convex operational framework and Segal's approach to quantum field theory. It is capable of encoding both classical and quantum (field) theories, implements spacetime locality in a manifest way and contains the complete modern notion of measurement in the quantum case. Its mathematical content can be condensed into a set of axioms that are similar to those of Atiyah and Segal.…
PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states, transformations, measurements and composition, which is a requirement for any physical theory. We aim to answer the question of whether a consistent physical theory with PT-symmetric observables extends standard quantum theory. We answer this question within the framework of general probabilistic theories, which is the most general framework for physical th…
Foundations of Relational Quantum Field Theory I: Scalars
University of Cambridge（剑桥大学）；Basic Research Community for Physics, Leipzig（莱比锡基础物理社区）；Institute for Quantum Optics and Quantum Information, Vienna（维也纳量子光学与量子信息研究所）；Department of Computer Science, University of Oxford（牛津大学计算机系）
Universal Operational Privacy in Distributed Quantum Sensing
Center for Quantum Technology, Korea Institute of Science and Technology (KIST)（韩国科学技术院量子技术中心）；Department of Physics, Yonsei University（延世大学物理系）；Division of Quantum Information, KIST School, Korea University of Science and Technology（韩国科学技术院KIST学院量子信息系）；Emerging Science and Technology Directorate, Agency for Defense Development（国防发展局新兴科技部）；Weapon Systems Engineering, ADD School, University of Science and Technology（韩国科学技术院ADD学校武器系统工程系）
We study hyper-decoherence in three operational theories from the literature, all examples of the recently introduced higher-order CPM construction. Amongst these, we show the theory of density hypercubes to be the richest in terms of post-quantum phenomena. Specifically, we demonstrate the existence of a probabilistic hyper-decoherence of density hypercubes to quantum systems and calculate the associated hyper-phase group. This makes density hypercubes of significant foundational interest, as an example of a theory which side-steps a recent no-go result in an original and unforeseen way, whil…
Classical and quantum mechanics across representations: an operational reading of the Wigner Weyl correspondence
University of Vienna, Faculty of Physics（维也纳大学物理学院）；Vienna Center for Quantum Science and Technology（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Constructor University（Constructor大学）；University of Geneva, Group of Applied Physics（日内瓦大学应用物理组）
It is a frequent assumption that - via superluminal information transfers - superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a 'no-go' theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operation…
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution we review recent developments towards a resource theory of contextuality and connections with operational applications of this property.
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase transitions. However, a comprehensive understanding of what actually constitutes topological order is still lacking. Here we show that one can interpret topological order as the ability of a system to perform topological error correction. We find that this operational approach corresponding to a measurable both lays the conceptual foundations for previous classific…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is fina…
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4,5]. However, this seems to run counter to results in two-dimensional systems, which allow for anyons, particles with statistics which interpolate between Fermi-Dirac and Bose-E…
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of probability distributions at the operational level, and thus may provide a dynamical explanation for Born's rule of quantum probabilities. This link between geometry and operational probabilities is argued to be a promising angle from which to study the potential for "hidden information" in quantum systems, and guide efforts in quantum foundations more gene…
Diamond quantum thermometry exploits the optical and electrical spin properties of colour defect centres in diamonds and, acts as a quantum sensing method exhibiting ultrahigh precision and robustness. Compared to the existing luminescent nanothermometry techniques, a diamond quantum thermometer can be operated over a wide temperature range and a sensor spatial scale ranging from nanometres to micrometres. Further, diamond quantum thermometry is employed in several application, including electronics and biology, to explore these fields with nanoscale temperature measurements. This review cover…
Operational theory for photonic circuits: generalizing linear optics beyond quantum theory
Naturwissenschaftlich-Technische Fakultät, Universität Siegen（锡根大学自然科学技术学院）；Department for Quantum Technology, Universität Münster（明斯特大学量子技术系）；Institut für Theoretische Physik, Leibniz Universität Hannover（汉诺威莱布尼茨大学理论物理研究所）
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalized.…
