Experimental minimum-error quantum-state discrimination in high dimensions

Abstract

Quantum mechanics forbids perfect discrimination among nonorthogonal states through a single shot measurement. To optimize this task, many strategies were devised that later became fundamental tools for quantum information processing. Here, we address the pioneering minimum-error (ME) measurement and give the first experimental demonstration of its application for discriminating nonorthogonal states in high dimensions. Our scheme is designed to distinguish symmetric pure states encoded in the transverse spatial modes of an optical field; the optimal measurement is performed by a projection onto the Fourier transform basis of these modes. For dimensions ranging from D = 2 to D = 21 and nearly 14000 states tested, the deviations of the experimental results from the theoretical values range from 0.3% to 3.6% (getting below 2% for the vast majority), thus showing the excellent performance of our scheme. This ME measurement is a building block for high-dimensional implementations of many quantum communication protocols, including probabilistic state discrimination, dense coding with nonmaximal entanglement, and cryptographic schemes.

13 pages, 13 figures

References in corpus (41)

• Quantum Cryptography
• On the Measurement of Qubits
• Quantum key distribution using gaussian-modulated coherent states
• Security of quantum key distribution using d-level systems
• Quantum Illumination with Gaussian States
• In defense of the epistemic view of quantum states: a toy theory
• Quantum State Discrimination
• Hybrid quantum repeater using bright coherent light
• Security Proof for Quantum Key Distribution Using Qudit Systems
• Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
• Closing the detection loophole in Bell experiments using qudits
• Generation of maximally entangled states of qudits using twin photons
• Quantum Reading of a Classical Digital Memory
• Maximum Confidence Quantum Measurements
• Real-Time Imaging of Quantum Entanglement
• Measurements on the reality of the wavefunction
• Optical realization of optimal unambiguous discrimination for pure and mixed quantum states
• Exceeding classical capacity limit in quantum optical channel
• Experimental quantum tomography of photonic qudits via mutually unbiased basis
• Weak randomness in device independent quantum key distribution and the advantage of using high dimensional entanglement
• Experimental realization of optimal detection strategies for overcomplete states
• Optimal conclusive teleportation of quantum states
• Probabilistic Super Dense Coding
• How ψ-epistemic models fail at explaining the indistinguishability of quantum states
• Applying the simplest Kochen-Specker set for quantum information processing
• Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes
• $\psi$-epistemic models are exponentially bad at explaining the distinguishability of quantum states
• Experimental Realization of Maximum Confidence State Discrimination for the Extraction of Quantum Information
• Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator
• Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
• Sequential projective measurements for channel decoding
• Distinguishing between non-orthogonal quantum states of a single spin
• Optimal Quantum States for Image Sensing in Loss
• Remote state preparation of spatial qubits
• Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array
• Maximum-confidence discrimination among symmetric qudit states
• Quantum teleportation via maximum-confidence quantum measurements
• Deterministic and probabilistic entanglement swapping of nonmaximally entangled states assisted by optimal quantum state discrimination
• Optimized generation of spatial qudits by using a pure phase spatial light modulator
• Discrimination with an error margin among three symmetric states of a qubit
• Distinguishability Measures and Ensemble Orderings

Cited by in corpus (29)

• Operational Resource Theory of Imaginarity
• High-dimensional quantum communication complexity beyond strategies based on Bell's theorem
• Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses
• Simultaneously sorting overlapping quantum states of light
• Photonic Discrete-time Quantum Walks and Applications
• Quantum receiver for phase-shift keying at the single photon level
• Quantum randomness protected against detection loophole attacks
• Experimental quantum channel discrimination using metastable states of a trapped ion
• Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference
• Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy
• Experimental investigation of wave-particle duality relations in asymmetric beam interference
• Quantum state discrimination in a PT-symmetric system
• Optimal control of coherent light scattering for binary decision problems
• Experimental quantum tomography assisted by multiply symmetric states in higher dimensions
• The Helstrom measurement: A nondestructive implementation
• Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies
• Quantum State Discrimination on Reconfigurable Noise-Robust Quantum Networks
• Controlled generation of mixed spatial qudits with arbitrary degree of purity
• Ptychography of pure quantum states
• Proposal for Automated Operations for Single-Photon Multipath Qudits
• Experimental optimal discrimination of $N$ states of a qubit with fixed rates of inconclusive outcomes
• Training quantum measurement devices to discriminate unknown non-orthogonal quantum states
• Ptychographic reconstruction of pure quantum states
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension
• Delayed-choice quantum erasers and the Einstein-Podolsky-Rosen paradox
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• Discrimination of metric theories
• Unbounded entanglement-sustaining sequential local quantum state discrimination