A causal modelling analysis of Bell scenarios in space-time: implications of jamming non-local correlations for relativistic causality principles

Bell scenarios involve space-like separated measurements made by multiple parties. The standard no-signalling constraints ensure that such parties cannot signal superluminally by choosing their measurement settings. In tripartite Bell scenarios, relaxed non-signalling constraints have been proposed, which permit a class of post-quantum theories known as jamming non-local theories. To analyse whether no superluminal signalling continues to hold in these theories and, more generally, the role of non-signalling constraints in preserving relativistic causality principles, we apply a framework that we have recently developed for defining information-theoretic causal models in non-classical theories and their compatibility with relativistic causality in a space-time. We show that any theory that generates jamming correlations in a Bell scenario between space-like separated parties must necessarily do so through causal fine-tuning and by means of superluminal causal influences. Moreover, within our framework, we show that jamming theories can also lead to superluminal signalling (contrary to previous claims) unless it is ensured that certain systems are fundamentally inaccessible to agents and their interventions. Finally, we analyse relativistic causality in Bell scenarios showing that no-signalling constraints on correlations are generally insufficient for ruling out superluminal signalling when general interventions are also allowed. In this way, we identify necessary and sufficient conditions for ruling out superluminal signalling in Bell scenarios, and demonstrate through examples that the non-signalling constraints on correlations are neither necessary nor sufficient for ruling out causal loops. These results solidify our understanding of relativistic causality principles in information processing tasks in space-time, involving classical, quantum or post-quantum resources.Comment: 25+14 pages. This paper contains improved versions of some (previously unpublished) results from V. Vilasini's PhD thesis arXiv:2102.02393. Comments welcome

Information-processing in theories constrained by no superluminal causation vs no superluminal signalling

Relativistic causality principles constrain information processing possibilities in space-time. No superluminal causation (NSC) and no superluminal signaling (NSS) are two such principles which, although related, are distinct. In this work we study the consequence of these principles by considering the tasks of generating non-classical correlations within two space-time configurations. Considering theories constrained by NSC, we show that the first task is impossible in any classical theory and the second is impossible in any (possibly non-classical) theory. However, we construct a protocol enabling non-classical correlations to be generated in both configurations in a theory restricted by the weaker NSS principle. To do so we exploit theories that allow an effect called jamming. In our realisation, non-communicating agents sharing classical resources and assisted by jamming, can generate PR-box correlations. Using this protocol the violation of NSC without violating NSS would be verifiable. We discuss the implications of these findings for the speed of generation of non-classical correlations. Our work offers insights into the differences in information processing power of theories constrained by NSC, NSS and other relativistic causality principles.Comment: 5 pages + appendix, 2 figures. This paper contains improved versions of initial results included in VV's PhD thesis arXiv:2102.0239

A general framework for consistent logical reasoning in Wigner's friend scenarios: subjective perspectives of agents within a single quantum circuit

It is natural to expect a complete physical theory to have the ability to consistently model agents as physical systems of the theory. In [Nat. Comms. 9, 3711 (2018)], Frauchiger and Renner (FR) claim to show that when agents in quantum theory reason about each other's knowledge in a certain Wigner's friend scenario, they arrive at a logical contradiction. In light of this, Renner often poses the challenge: provide a set of reasoning rules that can be used to program quantum computers that may act as agents, which are (a) logically consistent (b) generalise to arbitrary Wigner's friend scenarios (c) efficiently programmable and (d) consistent with the temporal order of the protocol. Here we develop a general framework where we show that every logical Wigner's friend scenario (LWFS) can be mapped to a single temporally ordered quantum circuit, which allows agents in any LWFS to reason in a way that meets all four criteria of the challenge. Importantly, our framework achieves this general resolution without modifying classical logic or unitary quantum evolution or the Born rule, while allowing agents' perspectives to be fundamentally subjective. We analyse the FR protocol in detail, showing how the apparent paradox is resolved there. We show that apparent logical contradictions in any LWFS only arise when ignoring the choice of Heisenberg cut in scenarios where this choice does matter, and taking this dependence into account will always resolve the apparent paradox. Our results establish that universal applicability of quantum theory does not pose any threat to multi-agent logical reasoning and we discuss the implications of these results for FR's no-go theorem. Moreover, our formalism suggests the possibility of a truly relational and operational description of Wigner's friend scenarios that is consistent with quantum theory as well as probability theory applied to measurement outcomes.Comment: 33 + 14 pages, 10 figure

Lean and BIM Implementation Barriers in New Zealand Construction Practice

fals

Composable security in relativistic quantum cryptography

Relativistic protocols have been proposed to overcome certain impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. However, composing such protocols with each other to construct new cryptographic resources is known to be insecure in some cases. To make general statements about such constructions, a composable framework for modelling cryptographic security in Minkowski space is required. Here, we introduce a framework for performing such a modular security analysis of classical and quantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and unbiased coin flipping can be constructed from a simple resource called channel with delay; (2) biased coin flipping, bit commitment and channel with delay through any classical, quantum or post-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is impossible to securely increase the delay of a channel, given several short-delay channels as ingredients. Results(1) and (3) imply in particular the non-composability of existing relativistic bit commitment and coin flipping protocols

Multi-agent paradoxes beyond quantum theory

Which theories lead to a contradiction between simple reasoning principles and modelling observers' memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory, with a thought experiment that leads to a multi-agent paradox. Here we generalize the conditions of the Frauchiger-Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box, which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers' memories may evolve in box world, in a way consistent with Barrett's criteria for allowed operations

Analyzing causal structures using Tsallis entropies

Understanding cause-effect relationships is a crucial part of the scientific process. As Bell’s theorem shows, within a given causal structure, classical and quantum physics impose different constraints on the correlations that are realisable, a fundamental feature that has technological applications. However, in general it is difficult to distinguish the set of classical and quantum correlations within a causal structure. Here we investigate a method to do this based on using entropy vectors for Tsallis entropies. We derive constraints on the Tsallis entropies that are implied by (conditional) independence between classical random variables and apply these to causal structures. We find that the number of independent constraints needed to characterise the causal structure is prohibitively high that the computations required for the standard entropy vector method cannot be employed even for small causal structures. Instead, without solving the whole problem, we find new Tsallis entropic constraints for the triangle causal structure by generalising known Shannon constraints. Our results reveal new mathematical properties of classical and quantum Tsallis entropies and highlight difficulties of using Tsallis entropies for analysing causal structures

Composable and Finite Computational Security of Quantum Message Transmission

Recent research in quantum cryptography has led to the development of schemes that encrypt and authenticate quantum messages with computational security. The security definitions used so far in the literature are asymptotic, game-based, and not known to be composable. We show how to define finite, composable, computational security for secure quantum message transmission. The new definitions do not involve any games or oracles, they are directly operational: a scheme is secure if it transforms an insecure channel and a shared key into an ideal secure channel from Alice to Bob, i.e., one which only allows Eve to block messages and learn their size, but not change them or read them. By modifying the ideal channel to provide Eve with more or less capabilities, one gets an array of different security notions. By design these transformations are composable, resulting in composable security. Crucially, the new definitions are finite. Security does not rely on the asymptotic hardness of a computational problem. Instead, one proves a finite reduction: if an adversary can distinguish the constructed (real) channel from the ideal one (for some fixed security parameters), then she can solve a finite instance of some computational problem. Such a finite statement is needed to make security claims about concrete implementations. We then prove that (slightly modified versions of) protocols proposed in the literature satisfy these composable definitions. And finally, we study the relations between some game-based definitions and our composable ones. In particular, we look at notions of quantum authenticated encryption and QCCA2, and show that they suffer from the same issues as their classical counterparts: they exclude certain protocols which are arguably secure.Comment: 43+11 pages, 18 figures, v2: minor changes, extended version of the published pape

A general framework for consistent logical reasoning in Wigner's friend scenarios: subjective perspectives of agents within a single quantum circuit

33 + 14 pages, 10 figuresIt is natural to expect a complete physical theory to have the ability to consistently model agents as physical systems of the theory. In [Nat. Comms. 9, 3711 (2018)], Frauchiger and Renner (FR) claim to show that when agents in quantum theory reason about each other's knowledge in a certain Wigner's friend scenario, they arrive at a logical contradiction. In light of this, Renner often poses the challenge: provide a set of reasoning rules that can be used to program quantum computers that may act as agents, which are (a) logically consistent (b) generalise to arbitrary Wigner's friend scenarios (c) efficiently programmable and (d) consistent with the temporal order of the protocol. Here we develop a general framework where we show that every logical Wigner's friend scenario (LWFS) can be mapped to a single temporally ordered quantum circuit, which allows agents in any LWFS to reason in a way that meets all four criteria of the challenge. Importantly, our framework achieves this general resolution without modifying classical logic or unitary quantum evolution or the Born rule, while allowing agents' perspectives to be fundamentally subjective. We analyse the FR protocol in detail, showing how the apparent paradox is resolved there. We show that apparent logical contradictions in any LWFS only arise when ignoring the choice of Heisenberg cut in scenarios where this choice does matter, and taking this dependence into account will always resolve the apparent paradox. Our results establish that universal applicability of quantum theory does not pose any threat to multi-agent logical reasoning and we discuss the implications of these results for FR's no-go theorem. Moreover, our formalism suggests the possibility of a truly relational and operational description of Wigner's friend scenarios that is consistent with quantum theory as well as probability theory applied to measurement outcomes