Device-independent certification of desirable properties with a confidence interval
arXiv:2401.06627 · doi:10.3389/fphy.2024.1434095
Abstract
In the development of quantum technologies, a reliable means for characterizing quantum devices is crucial. However, the conventional approach based on, e.g., quantum state tomography or process tomography relies on assumptions often not necessarily justifiable in a realistic experimental setting. While the device-independent approach to this problem bypasses the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where i.i.d. trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based-ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval. To illustrate the versatility of these methods, we demonstrate how we can use them to certify, with finite data, the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we give examples showing how the amount of certifiable negativity and fidelity scales with the number of trials, and how many experimental trials one needs to certify a qutrit state space, or the presence of genuine tripartite entanglement. Overall, we have found that the PBR protocol and the martingale-based protocol often offer similar performance, even though the former does have to presuppose any witness. In contrast, our findings also show that the performance of the martingale-based protocol may be severely affected by one's choice of the witness. Intriguingly, a witness useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.
v3: Essentially published version; v2: 13+5 pages, 16 figures (results strengthened, typos corrected); v1: 13+3 pages, 14 figures
References in corpus (73)
- Quantum entanglement
- Quantum Cryptography
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Quantum cryptography: Public key distribution and coin tossing
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- Device-independent security of quantum cryptography against collective attacks
- Violation of Bell's inequality under strict Einstein locality conditions
- Significant-loophole-free test of Bell's theorem with entangled photons
- Random Numbers Certified by Bell's Theorem
- A strong loophole-free test of local realism
- Bell inequalities for arbitrarily high dimensional systems
- Violation of Bell inequalities by photons more than 10 km apart
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- From Bell's Theorem to Secure Quantum Key Distribution
- Non-local correlations as an information theoretic resource
- Device-independent quantum key distribution secure against collective attacks
- Bounding the set of quantum correlations
- Entanglement and Extreme Spin Squeezing
- Self-testing of quantum systems: a review
- Quantum certification and benchmarking
- Quantum non-locality in two three-level systems
- Testing the Hilbert space dimension
- Device-independent witnesses of genuine multipartite entanglement
- Multipartite entanglement in spin chains
- The definition of multipartite nonlocality
- Device-independent entanglement quantification and related applications
- Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
- Security of practical private randomness generation
- Simple and tight device-independent security proofs
- More Randomness from the Same Data
- Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
- Robust and versatile black-box certification of quantum devices
- Entropy accumulation
- Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
- Quantum nonlocality, Bell inequalities and the memory loophole
- Physical characterization of quantum devices from nonlocal correlations
- Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
- Evaluation of convex roof entanglement measures
- Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
- Family of Bell-like inequalities as device-independent witnesses for entanglement depth
- Asymptotically optimal data analysis for rejecting local realism
- Certifying the building blocks of quantum computers from Bell's theorem
- Self-testing entangled measurements in quantum networks
- Bounds on Quantum Correlations in Bell Inequality Experiments
- Device-independent point estimation from finite data and its application to device-independent property estimation
- Efficient quantification of experimental evidence against local realism
- Noise-resistant device-independent certification of Bell state measurements
- When quantum tomography goes wrong: drift of quantum sources and other errors
- Certifying experimental errors in quantum experiments
- Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses
- Generalised entropy accumulation
- Time, Finite Statistics, and Bell's Fifth Position
- Device-independent characterization of quantum instruments
- Sample-efficient device-independent quantum state verification and certification
- Quantifying multipartite nonlocality via the size of the resource
- Device-independent randomness generation from several Bell estimators
- Chained Bell Inequality Experiment with High-Efficiency Measurements
- Device-independent tests of structures of measurement incompatibility
- A weak form of self-testing
- Non-Locality of Experimental Qutrit Pairs
- Device-independent Certification of One-shot Distillable Entanglement
- Quantum Randomness Generation by Probability Estimation with Classical Side Information
- Self-testing with finite statistics enabling the certification of a quantum network link
- Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
- Device-independent quantification of measurement incompatibility
- Bounding the plausibility of physical theories in a device-independent setting via hypothesis testing
- Maximal Violation of a Broad Class of Bell Inequalities and Its Implications on Self-Testing
- Towards the device-independent certification of a quantum memory
- Naturally restricted subsets of nonsignaling correlations: typicality and convergence
- Regularising data for practical randomness generation
- Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials