arXiv subjects

Matthias Salzger

Publications and source records attributed to Matthias Salzger.

6 recordsLinked to original sources

arXiv2026

Superluminal Quantum Reference Frames

While particles cannot travel faster than the speed of light, nor can information, this assumption has over the years been frequently questioned. Most recently, it has been argued [New J. Phys. 22, 033038 (2020)] that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. We also discuss Bell experiments under superluminal quantum reference frame transformations, showing that involved probabilities remain conserved.

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arXiv2026

Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order

In quantum causality and quantum information, there is a vast landscape of abstract quantum protocols permitting cyclic or non-acyclic causal structures between operations, including frameworks for indefinite causal order and higher-order quantum processes such as process matrices. A longstanding open question is what is the largest class of abstract processes that admit physical realisations without post-selection. In this work, we provide a rigorous answer using a top-down approach grounded in relativistic causality principles. Building on the framework of causal boxes, which characterise the most general quantum information-processing protocols compatible with fixed background spacetimes, we formalise additional constraints (Acting Once + Local Order) capturing the closed-laboratory assumptions of the process matrix framework at a fine-grained spacetime level. We prove that any protocol in a classical acyclic spacetime satisfying these conditions is behaviourally equivalent to a quantum circuit with quantum control of causal order (QC-QC), providing a top-down derivation of QC-QCs from physical principles. Our results show that QC-QCs constitute precisely the class of higher-order quantum processes, including those with indefinite order, that can be physically realised within classical spacetime, ruling out more general non-causal processes under the closed-labs assumption. This clarifies the relationship between abstract higher-order process matrix frameworks and experimentally accessible quantum protocols, as well as the interplay between coarse-grained cyclic and fine-grained acyclic operational causal structures. We also develop characterisation techniques for process box protocols that lead to new causality-based open questions concerning spacetime quantum protocols and relativistic quantum experiments.

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arXiv2025

A decompositional framework for process theories in spacetime

There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.

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arXiv2025

A structure theorem for complex-valued quasiprobability representations of physical theories

Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and quantum sensing. While traditional quasiprobability representations typically employ real-valued distributions, recent developments highlight the usefulness of complex-valued ones -- most notably, via the family of Kirkwood--Dirac quasiprobability distributions. Building on the framework of Schmid et al. [Quantum 8, 1283 (2024)], we extend the analysis to encompass complex-valued quasiprobability representations that need not preserve the identity channel. Additionally, we also extend previous results to consider mappings towards infinite-dimensional spaces. We show that, for each system, every such representation can be expressed as the composition of two maps that are completely characterized by their action on states and on the identity (equivalently, on effects) for that system. Our results apply to all complex-valued quasiprobability representations of any finite-dimensional, tomographically-local generalized probabilistic theory, with finite-dimensional quantum theory serving as a paradigmatic example. In the quantum case, the maps' action on states and effects corresponds to choices of frames and dual frames for the representation. This work offers a unified mathematical framework for analyzing complex-valued quasiprobability representations in generalized probabilistic theories.

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arXiv2024

Mapping indefinite causal order processes to composable quantum protocols in a spacetime

Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents' operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC's behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure.

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arXiv2023

Connecting indefinite causal order processes to composable quantum protocols in a spacetime

Process matrices are a framework to model causal relations in the absence of a well-defined acyclic causal order. The framework is very general and does not even assume the existence of a background spacetime. As a result, it is an open question how the framework should be interpreted physically and how and even if composition can be defined. On the other hand, so-called causal boxes define a framework that allows for arbitrary composition. In this work, we treat quantum circuits with quantum control of causal order (QC-QC), a subset of process matrices, which can be interpreted as generalized quantum circuits, and process box, a subset of causal boxes, which can be interpreted as processes. We analyze their state spaces and define a notion of operational equivalence between QC-QCs and process boxes based on this analysis. We then explicitly construct for each QC-QC an operationally equivalent process box. This allows us to define composition of QC-QCs in terms of composition of causal boxes which is well-defined. We further show that process boxes admit a unitary extension and conjecture that the background spacetime can be assumed to have a specific simple form. Based on this conjecture, we construct an operationally equivalent QC-QC for each process box. Our results indicate that the only class of processes that can be physically implemented in a fixed background spacetime are those that can be interpreted as quantum circuits with quantum controlled superpositions of orders. Further, they also reveal that the composability issue can be resolved by embedding processes in a spacetime structure. This in turn sheds light on the connection between physical realizability in a spacetime and composability.

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