Discrimination of Quantum Channels
type: CreativeWork
description: This thesis deals with assessing optimal decision strategies and error rates for the task of binary quantum channel discrimination, where the main focus lies on proving optimal asymmetric error exponents (both asymptotically and non-asymptotically) for different variants of this problem. The task of binary quantum channel discrimination is to distinguish a quantum channel (a quantum device with a quantum input and a quantum output), of which n identical copies of are given, into one of two classes. In the simplest instance the task is just to recognize the channel as one of two possible options. Even when the n copies of the channel are assumed to be independent and identically distributed (i.i.d.), the optimal joint input states will often be entangled, and hence this becomes a highly non-trivial non-i.i.d. hypothesis testing problem, which in certain cases can also be shown to require adaptivity for optimal discrimination performance. This thesis works on exploring the landscape of when adaptivity is helpful, and what can be said about optimal asymmetric error rates in various regimes. Concretely, first, in the already mentioned simple case of distinguishing between two single options, and for arbitrary (finite) number of channel uses, we prove a relation between the error rates of optimal adaptive and non-adaptive (so called parallel) strategies, with a mostly explicit construction of a "good" parallel strategy (in a certain quantified sense) given an adaptive one. Additionally, we show how optimal parallel strategies and error rates can be computed as a semi-definite program (SDP) that grows only polynomially in n. Next, we study the problem of composite channel discrimination, where the two classes to distinguish between can now be very general sets of channels, and which to our knowledge has so far not been studied even classically, despite its broad applicability to real-world discrimination tasks. Also here, we establish asymptotic asymmetric error exponents…
abstract: This thesis deals with assessing optimal decision strategies and error rates for the task of binary quantum channel discrimination, where the main focus lies on proving optimal asymmetric error exponents (both asymptotically and non-asymptotically) for different variants of this problem. The task of binary quantum channel discrimination is to distinguish a quantum channel (a quantum device with a quantum input and a quantum output), of which n identical copies of are given, into one of two classes. In the simplest instance the task is just to recognize the channel as one of two possible options. Even when the n copies of the channel are assumed to be independent and identically distributed (i.i.d.), the optimal joint input states will often be entangled, and hence this becomes a highly non-trivial non-i.i.d. hypothesis testing problem, which in certain cases can also be shown to require adaptivity for optimal discrimination performance. This thesis works on exploring the landscape of when adaptivity is helpful, and what can be said about optimal asymmetric error rates in various regimes. Concretely, first, in the already mentioned simple case of distinguishing between two single options, and for arbitrary (finite) number of channel uses, we prove a relation between the error rates of optimal adaptive and non-adaptive (so called parallel) strategies, with a mostly explicit construction of a "good" parallel strategy (in a certain quantified sense) given an adaptive one. Additionally, we show how optimal parallel strategies and error rates can be computed as a semi-definite program (SDP) that grows only polynomially in n. Next, we study the problem of composite channel discrimination, where the two classes to distinguish between can now be very general sets of channels, and which to our knowledge has so far not been studied even classically, despite its broad applicability to real-world discrimination tasks. Also here, we establish asymptotic asymmetric error exponents…
author: Bergh, Bjarne
language: eng
keywords: Hypothesis testing, Quantum channel discrimination, Quantum channels, Quantum information theory
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/bf1c8a60-047b-4e22-bc8b-31c5402ecb01/download
license: https://creativecommons.org/licenses/by-sa/4.0/
date published: 2024-09-30
date modified: 2026-07-22T22:24:28Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.116951