Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

Abstract

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. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.

arXiv comment18 pages + Appendices

References in corpus (15)

• Quantum correlations with no causal order
• Quantum computations without definite causal structure
• Bloch vectors for qudits
• Experimental Superposition of Orders of Quantum Gates
• Experimental Verification of an Indefinite Causal Order
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Witnessing causal nonseparability
• Bell's Theorem for Temporal Order
• The Lense--Thirring Effect and Mach's Principle
• Communication through quantum-controlled noise
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Quantum-coherent mixtures of causal relations
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• Semi-device-independent certification of indefinite causal order
• On time and space double-slit experiments

Cited by in corpus (34)

• Communication through coherent control of quantum channels
• Quantum circuits with classical versus quantum control of causal order
• Cyclic Quantum Causal Models
• Quantum Temporal Superposition: the case of QFT
• Work extraction from coherently activated maps via quantum switch
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Thermal devices powered by generalized measurements with indefinite causal order
• Causal structure in the presence of sectorial constraints, with application to the quantum switch
• Quantum teleportation with relativistic communication from first principles
• Semi-device-independent certification of indefinite causal order in a photonic quantum switch
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Experimental superposition of time directions
• Indefinite Causal Orders from Superpositions in Time
• Experimental demonstration of input-output indefiniteness in a single quantum device
• Quantum metrology in the finite-sample regime
• Comparing the quantum switch and its simulations with energetically-constrained operations
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Fundamental limits for realising quantum processes in spacetime
• Quantum switch in the gravity of Earth
• Equivalence Principle in Classical and Quantum Gravity
• Gravitational quantum switch on a superposition of spherical shells
• Transmission of quantum information through quantum fields in curved spacetimes
• Indefinite causal order and quantum coordinates
• The Unruh-DeWitt model and its joint interacting Hilbert space
• Superpositions of thermalisations in relativistic quantum field theory
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Topological obstructions to quantum computation with unitary oracles
• Operational interpretation of the vacuum and process matrices for identical particles
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• Causal nonseparability and its implications for spatiotemporal relations
• A spacetime-covariant approach to inertial and accelerated quantum clocks in first-quantization
• Knot invariants and indefinite causal order
• Causality in a qubit-based quantum switch