Ultimate limits of approximate unambiguous discrimination
arXiv:2010.15753 · doi:10.1103/PhysRevResearch.2.043276
Abstract
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states are relatively well-understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood. Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown. In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels. In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols. For the special class of `teleportation-covariant' channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.
arXiv comment14 pages, 9 figures
References in corpus (58)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- Quantum sensing
- Advances in Quantum Metrology
- Fundamental Limits of Repeaterless Quantum Communications
- General Benchmarks for Quantum Repeaters
- A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application
- Advances in Photonic Quantum Sensing
- Quantum Illumination with Gaussian States
- Microwave Quantum Illumination
- Quantum Illumination at the Microwave Wavelengths
- Probabilistic cloning and identification of linearly independent quantum states
- Quantum enhanced positioning and clock synchronization
- Quantum State Discrimination
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Programmable quantum gate arrays
- Distributed quantum sensing in a continuous variable entangled network
- Multi-parameter estimation in networked quantum sensors
- Entanglement-Enhanced Sensing in a Lossy and Noisy Environment
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement
- Distributed Quantum Metrology and the Entangling Power of Linear Networks
- Optimum mixed-state discrimination for noisy entanglement-enhanced sensing
- Quantum Reading of a Classical Digital Memory
- Unambiguous state discrimination in quantum cryptography with weak coherent states
- Asymptotic teleportation scheme as a universal programmable quantum processor
- Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
- Maximum Confidence Quantum Measurements
- Unambiguous discrimination of mixed states
- Theory of channel simulation and bounds for private communication
- Entanglement can enhance the distinguishability of entanglement-breaking channels
- Optimal discrimination of mixed quantum states involving inconclusive results
- Fundamental limits to quantum channel discrimination
- Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology
- Unambiguous discrimination among quantum operations
- Ultimate Precision of Adaptive Noise Estimation
- Unambiguous discrimination between quantum mixed states
- Optimal estimation of quantum dynamics
- Mixed quantum state detection with inconclusive results
- General Strategies for Discrimination of Quantum States
- Distributed quantum sensing enhanced by continuous-variable error correction
- Optimum Unambiguous Discrimination of Linearly Independent Pure States
- Ultimate limits for multiple quantum channel discrimination
- State discrimination with error margin and its locality
- Entanglement-Assisted Absorption Spectroscopy
- Entanglement-enhanced testing of multiple quantum hypotheses
- Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination
- Quantum Metrology Assisted with Abstention
- Optimization and learning of quantum programs
- Convex optimization of programmable quantum computers
- Optimum unambiguous discrimination of two mixed states and application to a class of similar states
- Generalized quantum state discrimination problems
- Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
- Optimal probabilistic estimation of quantum states
- Structural approach to unambiguous discrimination of two mixed quantum states
- Unambiguous discrimination of linearly independent pure quantum states: Optimal average probability of success
- Optimal parameter estimation with a fixed rate of abstention
- Cost of postselection in decision theory
- Finding optimal solutions for generalized quantum state discrimination problems