Quantum verification and estimation with few copies

Abstract

As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges in the employment of such systems for reliable quantum information processing. Though the most complete technique is undoubtedly full tomography, the inherent exponential increase of experimental and post-processing resources with system size makes this approach infeasible even at moderate scales. For this reason, there is currently an urgent need to develop novel methods that surpass these limitations. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity), and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography, which enables the estimation of arbitrary elements of an unknown state with a number of copies that is low and independent of the system's size. These hyper-efficient techniques define a dimensional demarcation for partial tomography and open a path for novel applications.

20 pages, 4 figures, review article, very close to the published version

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Entanglement detection
• Quantum computational advantage using photons
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Device-independent security of quantum cryptography against collective attacks
• Strong quantum computational advantage using a superconducting quantum processor
• Multi-party entanglement in graph states
• Randomized Benchmarking of Quantum Gates
• Experimental entanglement of six photons in graph states
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Direct Fidelity Estimation from Few Pauli Measurements
• Evenly distributed unitaries: on the structure of unitary designs
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Entanglement Certification $-$ From Theory to Experiment
• Entanglement Detection in the Stabilizer Formalism
• Multipartite entanglement in spin chains
• Experimental Verification of Multipartite Entanglement in Quantum Networks
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Device-independent certification of entangled measurements
• Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
• Detecting quantum entanglement with unsupervised learning
• Sample-efficient device-independent quantum state verification and certification
• A perspective on few-copy entanglement detection in experiments

Cited by in corpus (12)

• Quantum networks self-test all entangled states
• Shadow tomography on general measurement frames
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Optimising quantum tomography via shadow inversion
• Collective Operations Can Exponentially Enhance Quantum State Verification
• Valid and efficient entanglement verification with finite copies of a quantum state
• A survey of universal quantum von Neumann architecture
• Holographic Classical Shadow Tomography
• Experimental Verification of Entangled States in the Adversarial Scenario
• Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases