In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. W…
We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the causal relationships between putative spacetime subsystems. Our analysis reveals a quantum generalization of the thermodynamic arrow of time and begins to explore the roles of entanglement, scrambling and quantum error correction in the emergence of spacetime. For instance, exotic causal relationships can arise due to dynamically induced quantum error correction …
In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present an algebraic framework that incorporates both finite- and infinite-dimensional systems including quantum fields. Thanks to the absence of a definite spacetime causal structure, Lagrangian quantum field theories can be studied on a quantum superposition of spacetimes with a point identification structure.
Processes with an indefinite causal structure may violate a causal inequality, which quantifies quantum correlations that arise from a lack of causal order. In this paper, we show that when the inequalities are analysed with a Gaussian-localised field theoretic definition of particles and labs, the causal indeterminacy of the fields themselves allows a causal inequality to be violated within the causal structure of Minkowski spacetime. We quantify the violation of the inequality and determine the optimal ordering of observers.
A Proposed Test of the Local Causality of Spacetime
一个支配时空中度规场和物质场的理论是{ \it local causal}，如果任何区域中场的概率分布完全由该区域过去的物理数据决定，也就是说，它与类空分离点上的事件无关。广义相对论显然是局部因果的，因为一个区域中的场完全由其过去的物理数据决定。人们自然会问，在其他可能的理论中，时空的基本描述是经典的和几何的--例如，将经典时空几何随机耦合到物质的量子场论的假设理论--是否也可能是局部因果的。另一方面，引力的量子理论应该允许在宏观水平上违反局域因果关系的时空的创造。本文描述了一个实验来检验时空的局域因果关系，从而检验引力是否像引力的量子理论所建议的那样在这方面表现。这个实验要么直接证明引力场不是局部因果的，从而证明量子引力是弱的;要么为量子理论的有效性确定一个明确的界限。
It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time $t$ gives rise to a distinguished state on the algebra generated by fermionic and bosonic field operators. The proof of positivity of the state is given and representations are constructed.
Impossibility of superluminal signalling rules out causal loops in conical spacetimes
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家数字与信息系统研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工学院）；Institut Néel（内尔研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）
Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子理论国际中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Université Grenoble Alpes, Inria（格勒诺布尔阿尔卑斯大学法国国家信息与自动化研究所）
After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", a…
The theory of causal fermion systems is a new physical theory which aims to describe a fundamental level of physical reality. Its mathematical core is the causal action principle. In this thesis, we develop a formalism which connects the causal action principle to a suitable notion of fields on space-time. We derive field equations from the causal action principle and find that the dynamics induced by the field equations conserve a symplectic form which gives rise to an Hamiltonian time evolution if the causal fermion system admits a notion of time. In this way, we establish the dynamics of ca…
