Quantum Verification and Estimation with Few Copies. Issue 5 (17th March 2022)

• Record Type: Journal Article
• Authors: Morris, Joshua; Saggio, Valeria; Gočanin, Aleksandra; Dakić, Borivoje
• Is Part Of: Advanced quantum technologies. Volume 5:Issue 5(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-03-17
• Subjects: few copies -- quantum entanglement -- quantum verification -- state tomography; Quantum theory -- Periodicals; Quantum computing -- Periodicals; Quantum chemistry -- Periodicals; Quantum electronics -- Periodicals; 537.5
• DOI: 10.1002/qute.202100118
• Languages: English
• ISSNs: 2511-9044

Abstract

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 represent 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. Abstract : This review summarizes recent work in the domain of quantum verification and estimation. With a focus on dimension‐independent sample complexity, presented are novel techniques applicable to quantum systems of arbitrary size. This work begins with efficient extraction of very simple tasks such as entanglement witnesses and closes with strategies for simultaneous estimation of exponentially many observables on a general quantum state.