On the definition and characterisation of multipartite causal (non)separability

Abstract

The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which---although a priori subtly different---turns out to be equivalent to the concept of "extensible causal (non)separability" introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability.

References in corpus (30)

• Quantum correlations with no causal order
• Classification of mixed three-qubit states
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Transforming quantum operations: quantum supermaps
• Experimental Superposition of Orders of Quantum Gates
• Computational advantage from quantum-controlled ordering of gates
• Experimental Verification of an Indefinite Causal Order
• Enhanced communication with the assistance of indefinite causal order
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• Indefinite Causal Order in a Quantum Switch
• The definition of multipartite nonlocality
• Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
• An operational framework for nonlocality
• Witnessing causal nonseparability
• Toward a general theory of quantum games
• Quantum superposition of the order of parties as a communication resource
• The simplest causal inequalities and their violation
• Quantum computation with programmable connections between gates
• Multipartite Causal Correlations: Polytopes and Inequalities
• Witnesses of causal nonseparability: an introduction and a few case studies
• Quantum communication in a superposition of causal orders
• Entanglement, non-Markovianity, and causal non-separability
• Causally nonseparable processes admitting a causal model
• Perfect signaling among three parties violating predefined causal order
• Indefinite causal structures for continuous-variable systems
• The entropic approach to causal correlations
• Process Products Need Qualification
• Genuinely Multipartite Noncausality
• Quantum Circuits for the Unitary Permutation Problem

Cited by in corpus (31)

• Communication through coherent control of quantum channels
• 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
• Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
• Communication Enhancement Through Quantum Coherent Control of $N$ Channels in an Indefinite Causal-order Scenario
• Quantum circuits with classical versus quantum control of causal order
• Cyclic Quantum Causal Models
• Experiments on quantum causality
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Quantification of quantum dynamics with input-output games
• Semi-device-independent certification of indefinite causal order
• Resource theory of causal connection
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Consequences of preserving reversibility in quantum superchannels
• Reassessing the advantage of indefinite causal orders for quantum metrology
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Classical communication through quantum causal structures
• Universal construction of decoders from encoding black boxes
• A no-go theorem for superpositions of causal orders
• The Multi-round Process Matrix
• Network-Device-Independent Certification of Causal Nonseparability
• Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
• Background Independence and Quantum Causal Structure
• Causal nonseparability and its implications for spatiotemporal relations
• Conditional probability and interferences in generalized measurements with or without definite causal order
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• A de Finetti theorem for quantum causal structures
• Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order