Witnesses of causal nonseparability: an introduction and a few case studies

Abstract

It was recently realised that quantum theory allows for so-called causally nonseparable processes, which are incompatible with any definite causal order. This was first suggested on a rather abstract level by the formalism of process matrices, which only assumes that quantum theory holds locally in some observers' laboratories, but does not impose a global causal structure; it was then shown, on a more practical level, that the quantum switch---a new resource for quantum computation that goes beyond causally ordered circuits---provided precisely a physical example of a causally nonseparable process. To demonstrate that a given process is causally nonseparable, we introduced in [Araújo et al., New J. Phys. 17, 102001 (2015)] the concept of witnesses of causal nonseparability. Here we present a shorter introduction to this concept, and concentrate on some explicit examples to show how to construct and use such witnesses in practice.

15 pages, 7 figures

References in corpus (6)

• Experimental Superposition of Orders of Quantum Gates
• Witnessing causal nonseparability
• Causal and causally separable processes
• Quantum superposition of the order of parties as a communication resource
• The simplest causal inequalities and their violation
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios

Cited by in corpus (38)

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• Indefinite Causal Order in a Quantum Switch
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• Experimental Quantum Communication Enhancement by Superposing Trajectories
• Computational advantage from quantum superposition of multiple temporal orders of photonic gates
• Communication through quantum-controlled noise
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Quantum circuits with classical versus quantum control of causal order
• Multipartite Causal Correlations: Polytopes and Inequalities
• Cyclic Quantum Causal Models
• On the definition and characterisation of multipartite causal (non)separability
• Experimental entanglement of temporal order
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• Quantification of quantum dynamics with input-output games
• Semi-device-independent certification of indefinite causal order
• The entropic approach to causal correlations
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Reassessing thermodynamic advantage from indefinite causal order
• Quantum communication through devices with indefinite input-output direction
• Anomalous Weak Values Without Post-Selection
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Separable and Inseparable Quantum Trajectories
• Monitored non-adiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants
• Indefinite causal order and quantum coordinates
• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Classical evolution in quantum systems
• Entanglement-assisted quantum speedup: Beating local quantum speed limits
• Network-Device-Independent Certification of Causal Nonseparability
• Entanglement for any definition of two subsystems
• Revisiting dynamics of quantum causal structures -- when can causal order evolve?
• Emergent non-Markovianity and dynamical quantification of the quantum switch
• Quantifying Causal Influence in Quantum Mechanics
• Quantum theory cannot violate a causal inequality
• Simulating violation of causality using a topological phase transition
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• No quantum advantage for violating fixed-order inequalities?
• Knot invariants and indefinite causal order