Causal influence versus signalling for interacting quantum channels
arXiv:2309.07771 · doi:10.1103/PhysRevResearch.6.043305
Abstract
A causal relation between quantum agents, say Alice and Bob, is necessarily mediated by an interaction. Modelling the last one as a reversible quantum channel, an intervention of Alice can have causal influence on Bob's system, modifying correlations between Alice and Bob's systems. Causal influence between quantum systems necessarily allows for signalling. Here we prove a mismatch between causal influence and signalling via direct computation of the two quantities for the Cnot gate. Finally we show a continuity theorem for causal effects of unitary channels: a channel has small causal influence iff it allows for small signalling.
arXiv comment5 pages, revtex4-2
References in corpus (25)
- Information Causality as a Physical Principle
- Quantum correlations with no causal order
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Quantum Circuits Architecture
- Computational advantage from quantum-controlled ordering of gates
- Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
- Quantum Channels with Memory
- Quantum theory based on real numbers can be experimentally falsified
- Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
- Causal and localizable quantum operations
- Quantum common causes and quantum causal models
- Causal and causally separable processes
- On the capacities of bipartite Hamiltonians and unitary gates
- Indefinite causal order enables perfect quantum communication with zero capacity channels
- Semicausal operations are semilocalizable
- On quantum non-signalling boxes
- Multipartite Causal Correlations: Polytopes and Inequalities
- Cyclic Quantum Causal Models
- Theoretical framework for Higher-Order Quantum Theory
- Causal Boxes: Quantum Information-Processing Systems Closed under Composition
- Quantum Causal Influence
- Cellular automata in operational probabilistic theories
- Causal influence in operational probabilistic theories
- Addressable quantum gates