Quantum superpositions of causal orders as an operational resource

Abstract

Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as resources for concrete information-theoretic tasks. Here, we take a step forward by deriving a complete operational framework for causal nonseparability as a resource. Our first contribution is a formal definition of quantum control of causal orders, a stronger form of causal nonseparability (with the celebrated quantum switch as best-known example) where the causal orders of events for a target system are coherently controlled by a control system. We then build a resource theory -- for both generic causal nonseparability and quantum control of causal orders -- with a physically-motivated class of free operations, based on process-matrix concatenations. We present the framework explicitly in the mindset with a control register. However, our machinery is versatile, being applicable also to scenarios with a target register alone. Moreover, an important subclass of our operations not only is free with respect to causal nonseparability and quantum control of causal orders but also preserves the very causal structure of causal processes. Hence, our treatment contains, as a built-in feature, the basis of a resource theory of quantum causal networks too. As applications, first, we establish a sufficient condition for pure-process free convertibility. This imposes a hierarchy of quantum control of causal orders with the quantum switch at the top. Second, we prove that causal-nonseparability distillation exists, i.e. we show how to convert multiple copies of a process with arbitrarily little causal nonseparability into fewer copies of a quantum switch. Our findings reveal conceptually new, unexpected phenomena, with both fundamental and practical implications.

arXiv commentMain text 11 pages, 3 figures, 20 pages total

References in corpus (44)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• Quantum correlations with no causal order
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Entanglement of pure states for a single copy
• Intrinsic randomness as a measure of quantum coherence
• Quantum Circuits Architecture
• The general structure of quantum resource theories
• Taming multiparticle entanglement
• Experimental Superposition of Orders of Quantum Gates
• A mathematical theory of resources
• Computational advantage from quantum-controlled ordering of gates
• Open-System Dynamics of Entanglement
• Experimental Verification of an Indefinite Causal Order
• Quantum causal modelling
• 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
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
• Quantum common causes and quantum causal models
• Conditions for coherence transformations under incoherent operations
• An operational framework for nonlocality
• Witnessing causal nonseparability
• The resource theory of steering
• Causal and causally separable processes
• Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity
• Bell's Theorem for Temporal Order
• The simplest causal inequalities and their violation
• A purification postulate for quantum mechanics with indefinite causal order
• Quantum-coherent mixtures of causal relations
• Noncontextual wirings
• Asymptotic entanglement transformation between W and GHZ states
• Nonlocality free wirings and the distinguishability between Bell boxes
• Causally nonseparable processes admitting a causal model
• Quantum superpositions of "common-cause" and "direct-cause" causal structures
• Process Products Need Qualification
• Composition rules for quantum processes: a no-go theorem

Cited by in corpus (11)

• Computational advantage from quantum superposition of multiple temporal orders of photonic gates
• Quantum circuits with classical versus quantum control of causal order
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Distillation of quantum steering
• Resource theory of causal connection
• Consequences of preserving reversibility in quantum superchannels
• Reassessing thermodynamic advantage from indefinite causal order
• Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability
• The Multi-round Process Matrix
• Exposure of subtle multipartite quantum nonlocality
• Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order