Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
arXiv:2105.13369 · doi:10.1063/5.0075919
Abstract
For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform the parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are, indeed, optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of unitary channels. Finally, we derive an absolute upper bound for the maximal probability of successfully discriminating any set of unitary channels with any number of copies for the most general strategies that are suitable for channel discrimination. Our bound is tight since it is saturated by sets of unitary channels forming a group k-design.
arXiv comment10 + 14 pages, 4 figures. Code available at https://github.com/mtcq/unitary_channel_discrimination
References in corpus (45)
- Quantum metrology
- Quantum metrology with nonclassical states of atomic ensembles
- Reference frames, superselection rules, and quantum information
- 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
- Statistical distinguishability between unitary operations
- Using entanglement improves precision of quantum measurements
- Perfect discrimination of no-signalling channels via quantum superposition of causal structures
- Quantum Channels with Memory
- Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
- Witnessing causal nonseparability
- Memory effects in quantum channel discrimination
- Optimal quantum learning of a unitary transformation
- Toward a general theory of quantum games
- Efficient use of quantum resources for the transmission of a reference frame
- Quantum superposition of the order of parties as a communication resource
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- The simplest causal inequalities and their violation
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
- Process POVM: A mathematical framework for the description of process tomography experiments
- Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
- Quantum circuits with classical versus quantum control of causal order
- A purification postulate for quantum mechanics with indefinite causal order
- The space of logically consistent classical processes without causal order
- Cyclic Quantum Causal Models
- Optimal probabilistic storage and retrieval of unitary channels
- Covariant quantum measurements which maximize the likelihood
- Probabilistic exact universal quantum circuits for transforming unitary operations
- On the definition and characterisation of multipartite causal (non)separability
- Unambiguous discrimination among oracle operators
- Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
- Semi-device-independent certification of indefinite causal order
- Single-shot discrimination of quantum unitary processes
- Maximum likelihood estimation for a group of physical transformations
- Consequences of preserving reversibility in quantum superchannels
- Optimal processing of reversible quantum channels
- Identification of a reversible quantum gate: assessing the resources
- Unitary-process discrimination with error margin
- Extended Quantum Color Coding
- Optimal quantum discrimination of single-qubit unitary gates between two candidates
- Equivalence determination of unitary operations
Cited by in corpus (25)
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
- Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
- Learning quantum states and unitaries of bounded gate complexity
- Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
- Query-optimal estimation of unitary channels in diamond distance
- Resource theory of causal connection
- Semi-device-independent certification of indefinite causal order in a photonic quantum switch
- Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
- Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
- Optimal universal quantum circuits for unitary complex conjugation
- Strategies for single-shot discrimination of process matrices
- Identifying quantum change points for Hamiltonians
- Indefinite Time Directed Quantum Metrology
- Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
- Toward an Experimental Device-Independent Verification of Indefinite Causal Order
- Indefinite causal order strategy does not improve the estimation of group action
- Simulating the quantum switch with quantum circuits is computationally hard
- Optimal quantum precision in noise estimation: Is entanglement necessary?
- Quantum Advantage in Storage and Retrieval of Isometry Channels
- Learning the structure of any Hamiltonian from minimal assumptions
- Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
- Optimal Hamiltonian recognition of unknown quantum dynamics
- Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
- No quantum advantage for violating fixed-order inequalities?