Optimal quantum discrimination of single-qubit unitary gates between two candidates
arXiv:2103.08208 · doi:10.1103/PhysRevA.104.022422
Abstract
We analyze a discrimination problem of a single-qubit unitary gate with two candidates, where the candidates are not provided with their classical description, but their quantum sample is. More precisely, there are three unitary quantum gates -- one target and one sample for each of the two candidates -- whose classical description is unknown except for their dimension. The target gate is chosen equally among the candidates. We obtain the optimal protocol that maximizes the expected success probability, assuming the Haar distribution for the candidates. This problem is originally introduced in Hillery et al. (J. Mod. Opt. 2010), which provides a protocol achieving 7/8 in the expected success probability based on the ``unitary comparison" protocol of Andersson et al. (J. Phys. A 2003). The optimality of the protocol has been an open question since then. We prove the optimality of the comparison protocol, implying that only one of the two samples (one for each candidate) is needed to achieve an optimal discrimination. The optimization includes protocols outside the scope of quantum testers due to the dynamic ordering of the sample and target gates within a given protocol.
arXiv comment11 pages, 3 figures; effectively published version; title changed from ver. 1
References in corpus (75)
- Advances in Quantum Metrology
- Quantum fingerprinting
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Quantum State Discrimination
- Quantum state discrimination and its applications
- Statistical distinguishability between unitary operations
- Using entanglement improves precision of quantum measurements
- Perfect discrimination of no-signalling channels via quantum superposition of causal structures
- Optimal discrimination of quantum operations
- Quantum information and precision measurement
- Memory effects in quantum channel discrimination
- All entangled states are useful for channel discrimination
- Optimal quantum learning of a unitary transformation
- Quantum machine learning for quantum anomaly detection
- The Perfect Distinguishability of Quantum Operations
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- Unambiguous discrimination among quantum operations
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Quantum learning and universal quantum matching machine
- A universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states
- Optimal estimation of quantum dynamics
- Comparison of two unknown pure quantum states
- Process POVM: A mathematical framework for the description of process tomography experiments
- Beyond the swap test: optimal estimation of quantum state overlap
- Quantum Template Matching
- Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation
- Local Distinguishability of Multipartite Unitary Operations
- Identification and Distance Measures of Measurement Apparatus
- Quantum pure-state identification
- Optimal quantum tomography for states, measurements, and transformations
- Unambiguous pure state identification without classical knowledge
- Programmable quantum state discriminators with simple programs
- Quantum learning: optimal classification of qubit states
- Strategies for optimal single-shot discrimination of quantum measurements
- Exact Identification of a Quantum Change Point
- Experimental Quantum Process Discrimination
- Quantum learning of coherent states
- Unsupervised classification of quantum data
- Optimal networks for Quantum Metrology: semidefinite programs and product rules
- Unambiguous coherent state identification: Searching a quantum database
- Entanglement in channel discrimination with restricted measurements
- Multi-copy programmable discrimination of general qubit states
- Unitary transformations can be identified locally
- Comparing the states of many quantum systems
- Retrodiction of Generalised Measurement Outcomes
- Optimal single shot strategies for discrimination of quantum measurements
- Programmable unknown quantum-state discriminators with multiple copies of program and data: A Jordan basis approach
- Real-time calibration of coherent-state receivers: learning by trial and error
- Unambiguous comparison of ensembles of quantum states
- Single-shot discrimination of quantum unitary processes
- Optimal universal learning machines for quantum state discrimination
- Bounds on amplitude damping channel discrimination
- Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation
- Local Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations Acting on Two-Qudits by LOCC
- Unambiguous comparison of quantum measurements
- Unambiguous comparison of unitary channels
- Discrimination of two-qubit unitaries via local operations and classical communication
- Exact Quantum Search by Parallel Unitary Discrimination Schemes
- Locality and nonlocality in quantum pure-state identification problems
- Ancilla dimension in quantum channel discrimination
- Optimal two-copy discrimination of quantum measurements
- Success probabilities for universal unambiguous discriminators between unknown pure states
- Comparison of unitary transforms
- Unitary-process discrimination with error margin
- Capability of local operations and classical communication for distinguishing bipartite unitary operations
- Linear-Optical Implementation of Perfect Discrimination between Single-bit Unitary Operations
- Unambiguous identification of coherent states II: Multiple resources
- Optimal entanglement-assisted discrimination of quantum measurements
- Distinguishing classically indistinguishable states and channels
- Sequential scheme for locally discriminating bipartite unitary operations without inverses
- Optimal quantum state identification with qudit-encoded unknown states
- Process estimation in qubit systems: a quantum decision theory approach
- Two Notes on Grover's Search: Programming and Discriminating
- Decision problems with quantum black boxes
- Optimal unambiguous comparison of two unknown squeezed vacua
Cited by in corpus (4)
- Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
- No-signalling constrains quantum computation with indefinite causal structure
- Discrimination and certification of unknown quantum measurements
- Optimal Hamiltonian recognition of unknown quantum dynamics