On the optimal certification of von Neumann measurements
arXiv:2009.06776 · doi:10.1038/s41598-021-81325-1
Abstract
In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. From our main result follow the conditions when two pure states, unitary operations and von Neumann measurements cannot be distinguished perfectly but still can be certified with a given statistical significance. Moreover, we show the connection between the certification of quantum channels or von Neumann measurements and the notion of -numerical range.
References in corpus (23)
- Quantum Computing in the NISQ era and beyond
- Theoretical framework for quantum networks
- Quantum certification and benchmarking
- Efficient experimental validation of photonic boson sampling against the uniform distribution
- On the experimental verification of quantum complexity in linear optics
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- Memory effects in quantum channel discrimination
- The Perfect Distinguishability of Quantum Operations
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- Reliable quantum certification for photonic quantum technologies
- Unambiguous discrimination among quantum operations
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Discrimination of two channels by adaptive methods and its application to quantum system
- Identification and Distance Measures of Measurement Apparatus
- Strategies for optimal single-shot discrimination of quantum measurements
- Efficient verification of Boson Sampling
- Quantum state discrimination bounds for finite sample size
- Parallel distinguishability of quantum operations
- Strong Converse and Stein's Lemma in the Quantum Hypothesis Testing
- Discrimination of two-qubit unitaries via local operations and classical communication
- Discrimination of POVMs with rank-one effects
- Statistical Benchmarking of Scalable Photonic Quantum Systems
- Efficient verification of bosonic quantum channels via benchmarking