Quantum circuits with classical versus quantum control of causal order

Abstract

Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum circuits. A systematic understanding of the physical interpretation of more general types of quantum supermaps--in particular, those incompatible with a definite causal structure--is however lacking. Here we identify two new types of circuits that naturally generalise the fixed-order case and that likewise correspond to distinct classes of quantum supermaps, which we fully characterise. We first introduce "quantum circuits with classical control of causal order", in which the order of operations is still well-defined, but not necessarily fixed in advance: it can in particular be established dynamically, in a classically-controlled manner, as the circuit is being used. We then consider "quantum circuits with quantum control of causal order", in which the order of operations is controlled coherently. The supermaps described by these classes of circuits are physically realisable, and the latter encompasses all known examples of physically realisable processes with indefinite causal order, including the celebrated "quantum switch". Interestingly, it also contains new examples arising from the combination of dynamical and coherent control of causal order, and we detail explicitly one such process. Nevertheless, we show that quantum circuits with quantum control of causal order can only generate "causal" correlations, compatible with a well-defined causal order. We furthermore extend our considerations to probabilistic circuits that produce also classical outcomes, and we demonstrate by an example how our characterisations allow us to identify new advantages for quantum information processing tasks that could be demonstrated in practice.

34+17 pages, 13 figures. V3: corrected the statement of Proposition 7, specifying that the process matrix $W$ itself has to be positive semidefinite

References in corpus (10)

• Quantum Circuits Architecture
• Transforming quantum operations: quantum supermaps
• Experimental Verification of an Indefinite Causal Order
• Process POVM: A mathematical framework for the description of process tomography experiments
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
• Sending classical information via three noisy channels in superposition of causal orders
• Multipartite Causal Correlations: Polytopes and Inequalities
• Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels
• Routed quantum circuits
• Transmitting quantum information by superposing causal order of mutually unbiased measurements

Cited by in corpus (45)

• Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
• Optimal Strategies of Quantum Metrology with a Strict Hierarchy
• Work extraction from coherently activated maps via quantum switch
• Using adaptiveness and causal superpositions against noise in quantum metrology
• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Noncausal Page-Wootters circuits
• Semi-device-independent certification of indefinite causal order in a photonic quantum switch
• Evading noise in multiparameter quantum metrology with indefinite causal order
• Unlimited non-causal correlations and their relation to non-locality
• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
• Reassessing the advantage of indefinite causal orders for quantum metrology
• Quantum Uncertainty Principles for Measurements with Interventions
• Reassessing thermodynamic advantage from indefinite causal order
• Strict hierarchy of optimal strategies for global estimations: Linking global estimations with local ones
• Existence of processes violating causal inequalities on time-delocalised subsystems
• 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
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Admissible Causal Structures and Correlations
• The quantum switch is uniquely defined by its action on unitary operations
• Quantum Supermaps are Characterized by Locality
• Network-Device-Independent Certification of Causal Nonseparability
• Addressable quantum gates
• Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
• Coherent control of the causal order of entanglement distillation
• The Möbius game and other Bell tests for relativity
• Indefinite Time Directed Quantum Metrology
• Consistent circuits for indefinite causal order
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• Emergent non-Markovianity and dynamical quantification of the quantum switch
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Quantum switch as a thermodynamic resource in the context of passive states
• Simulating the quantum switch with quantum circuits is computationally hard
• Causal nonseparability and its implications for spatiotemporal relations
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Optimal quantum metrology under energy constraints
• Optimal Thermalization under Indefinite Causal Order with Identical and Asymmetric Baths
• Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
• No quantum advantage for violating fixed-order inequalities?
• Estimation of multivariate traces of states given partial classical information
• Knot invariants and indefinite causal order
• A Profunctorial Semantics for Quantum Supermaps