We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance.The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound with experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution.Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation.This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of an hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics.
A paramount topic in quantum foundations, rooted in the study of the EPR paradox and Bell inequalities, is that of characterizing quantum theory in terms of the space-like correlations it allows. Here we show that to focus only on space-like correlations is not enough: we explicitly construct a toy model theory that, while not contradicting classical and quantum theories at the level of space-like correlations, still displays an anomalous behavior in its time-like correlations. We call this anomaly, quantified in terms of a specific communication game, the "hypersignaling" phenomena. We hence conclude that the "principle of quantumness," if it exists, cannot be found in space-like correlations alone: nontrivial constraints need to be imposed also on time-like correlations, in order to exclude hypersignaling theories.One of the main tenets in modern physics is that if two space-like separated events are correlated, then such correlations must not carry any information [1]. This assumption, constituting the so-called no-signaling principle, was the starting point used by Bell [2] to quantify and compare space-like correlations of different theories on even grounds-an idea of vital importance for his argument about the EPR paradox [3] and the derivation of his famous inequality. Subsequently, due to seminal works by Tsirelson (Cirel'son) [4] and Popescu and Rohrlich [5], it became clear that the no-signaling principle alone is not enough to characterize "physical" space-like correlations: non-signaling space-like correlations allowed by quantum theory form a strict subset within the set of all non-signaling correlations [6].A natural question is then to try to identify additional principles that, together with the no-signaling principle, may be able to rule out all super-quantum non-signaling correlations at once. Various ideas have been proposed, ranging from complexity theory, e.g. the collapse of the complexity tower [7] to information theory, e.g. the information causality principle [8]. However, none of these has been able to characterize the quantum/superquantum boundary in full. In particular, an outstanding open question is whether quantum theory can be characterized in terms of the space-like correlations it allows [6].In this paper, we show that this cannot be done: any approach to characterize quantum theory based only on space-like correlations is necessarily incomplete unless it also takes into account time-like correlations as well. Our approach, which is completely unrelated to the study of temporal correlationsà la Leggett-Garg [9-12], considers the elementary resource of noiseless commu- * cqtmda@nus.edu.sg † sbrandse@caltech.edu ‡ alessandro.tosini@unipv.it § buscemi@is.nagoya-u.ac.jp ¶ phyvv@nus.edu.sg nication and the input/output correlations that can be so established. By analogy with the no-signaling principle, we operationally introduce what we call the "nohypersignaling principle," which roughly states that any input/output correlation that can be obtained by transmitting a composite system...
We show that the computational model based on local Fermionic modes in place of qubits does not satisfy local tomography and monogamy of entanglement, and has mixed states with maximal entanglement of formation. These features directly follow from the parity superselection rule. We generalize quantum superselection rules to general probabilistic theories as sets of linear constraints on the convex set of states. We then provide a link between the cardinality of the superselection rule and the degree of holism of the resulting theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.