Fundamental limits to quantum channel discrimination
arXiv:1803.02834 · doi:10.1038/s41534-019-0162-y
Abstract
What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation.
arXiv commentClose to published version. Main Text, Methods, and Supplementary Information all in a single file. 21 pages and 4 figures. REVTeX. Co-author added
References in corpus (49)
- Advances in Quantum Metrology
- Gaussian Quantum Information
- Fundamental Limits of Repeaterless Quantum Communications
- General Benchmarks for Quantum Repeaters
- Advances in Photonic Quantum Sensing
- Quantum Illumination with Gaussian States
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- The Quantum Chernoff Bound
- Quantum Illumination at the Microwave Wavelengths
- Microwave Quantum Illumination
- Quantum enhanced measurements without entanglement
- Experimental realisation of quantum illumination
- Programmable quantum gate arrays
- End-to-end capacities of a quantum communication network
- Entanglement-Enhanced Sensing in a Lossy and Noisy Environment
- Statistical distinguishability between unitary operations
- Asymptotic Error Rates in Quantum Hypothesis Testing
- Quantum Reading of a Classical Digital Memory
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Quantum information and precision measurement
- Ultimate precision bound of quantum and sub-wavelength imaging
- Quantum illumination versus coherent-state target detection
- Asymptotic teleportation scheme as a universal programmable quantum processor
- Computable bounds for the discrimination of Gaussian states
- The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
- Entanglement's Benefit Survives an Entanglement-Breaking Channel
- Theory of channel simulation and bounds for private communication
- Entanglement can enhance the distinguishability of entanglement-breaking channels
- Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
- Unambiguous discrimination among quantum operations
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Quantum teleportation scheme by selecting one of multiple output ports
- Ultimate Precision of Adaptive Noise Estimation
- Discrimination of two channels by adaptive methods and its application to quantum system
- General bounds for sender-receiver capacities in multipoint quantum communications
- How Discord underlies the Noise Resilience of Quantum Illumination
- Quantum Reading Capacity
- The minimum error probability of quantum illumination
- Optimal detection of losses by thermal probes
- Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy
- Experimental implementation of unambiguous quantum reading
- Asymmetric quantum hypothesis testing with Gaussian states
- Almost all quantum channels are equidistant
- Simulation of non-Pauli Channels
- Finite-resource teleportation stretching for continuous-variable systems
- Higher-dimensional performance of port-based teleportation
- Teleportation simulation of bosonic Gaussian channels: Strong and uniform convergence
- Cryptographic aspects of quantum reading
- Discriminating quantum field theories in non-inertial frames
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- Advances in Quantum Cryptography
- Advances in Photonic Quantum Sensing
- End-to-end capacities of a quantum communication network
- A Geometric Perspective on Quantum Parameter Estimation
- Operational Resource Theory of Quantum Channels
- Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
- Entanglement-Based Quantum Information Technology
- Fundamental limits of quantum illumination
- The quantum limit to incoherent imaging is achieved by linear interferometry
- Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
- A chain rule for the quantum relative entropy
- Fundamental limitations on distillation of quantum channel resources
- Quantum advantages for Pauli channel estimation
- Ultimate limits for multiple quantum channel discrimination
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Shadow process tomography of quantum channels
- Optical quantum super-resolution imaging and hypothesis testing
- Quantifying the resource content of quantum channels: An operational approach
- No-go theorems for quantum resource purification II: new approach and channel theory
- Quantum-enhanced Doppler lidar
- Quantum limits of superresolution in a noisy environment
- Optimization and learning of quantum programs
- Convex optimization of programmable quantum computers
- Subwavelength quantum imaging with noisy detectors
- Causal limit on quantum communication
- Experimental quantum reading with photon counting
- Quantum illumination via quantum-enhanced sensing
- Experimental Quantum Target Detection Approaching the Fundamental Helstrom Limit
- Multiparty orthogonal product states with minimal genuine nonlocality
- Asymptotic performance of port-based teleportation
- Quantum illumination receiver using double homodyne detection
- Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases
- Efficient multi port-based teleportation schemes
- Usefulness of adaptive strategies in asymptotic quantum channel discrimination
- Bounds on amplitude damping channel discrimination
- Mixed State Entanglement Classification using Artificial Neural Networks
- Generalization of port-based teleportation and controlled teleportation capability
- Characterising port-based teleportation as a universal simulator of qubit channels
- Multiport based teleportation -- transmission of a large amount of quantum information
- Programmability of covariant quantum channels
- Conditional channel simulation
- Optimality of the pretty good measurement for port-based teleportation
- Ultimate Limits of Thermal Pattern Recognition
- Optimal Multi-port-based Teleportation Schemes
- Quantum-machine-learning channel discrimination
- Quantum advantage for noisy channel discrimination
- Discriminating qubit amplitude damping channels
- Multiple-shot and unambiguous discrimination of von Neumann measurements
- Postselected quantum hypothesis testing
- Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
- Generalized quantum process discrimination problems
- Quantum illumination using polarization-path entangled single photons for low reflectivity object detection in noisy background
- Finding the optimal probe state for multiparameter quantum metrology using conic programming
- The maximum advantage of quantum illumination
- Limitations of Classically-Simulable Measurements for Quantum State Discrimination
- Local Quantum State Marking
- An agnostic-Dolinar receiver for coherent states classification
- Simple upper and lower bounds on the ultimate success probability for discriminating arbitrary finite-dimensional quantum processes
- Quantum Hypothesis Testing with Group Structure
- Optimal environment localization
- Minimal Port-based Teleportation
- Single-shot Quantum Signal Processing Interferometry
- No-signalling constrains quantum computation with indefinite causal structure
- Quantum readout of imperfect classical data
- Space-time generalization of mutual information
- Infinite-Dimensional Programmable Quantum Processors
- Identifying quantum change points for Hamiltonians
- Continuous variable port-based teleportation
- An introductory review on resource theories of generalized nonclassical light
- Analytical Bounds for Dynamic Multi-Channel Discrimination
- Idler-Free Multi-Channel Discrimination via Multipartite Probe States
- Polar Codes for Quantum Reading
- Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
- Port-based entanglement teleportation via noisy resource states
- Ultimate limits of approximate unambiguous discrimination
- On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
- Operation fidelity explored by numerical range of Kraus operators
- Teleportation of Post-Selected Quantum States
- Robust projective measurements through measuring code-inspired observables
- Excluding false negative error in certification of quantum channels
- Towards the ultimate limits of quantum channel discrimination and quantum communication
- Improving quantum channel discrimination with resourceful states
- Indefinite causal order strategy does not improve the estimation of group action
- Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
- Limitation of maximally entangled probes for single-shot distinguishability of unitaries
- Adversarial quantum channel discrimination
- Port-Based State Preparation and Applications
- From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications
- Asymptotic teleportation schemes bridging between standard and port-based teleportation
- Bounding the benefit of adaptivity in quantum metrology using the relative fidelity
- Efficient and operational quantifier of non-divisibility in terms of channel discrimination
- Optimal Hamiltonian recognition of unknown quantum dynamics
- Principles of quantum functional testing
- Square-root measurements and degradation of the resource state in port-based teleportation scheme
- On the distinguishability of geometrically uniform quantum states
- Multi-Armed Bandits and Quantum Channel Oracles
- A resource theory of asynchronous quantum information processing