## Dissertations, Theses, and Capstone Projects

## Date of Degree

9-2019

## Document Type

Dissertation

## Degree Name

Ph.D.

## Program

Physics

## Advisor

Janos Bergou

## Committee Members

Mark Hillery

Edgar Feldman

Neepa Maitra

Christopher Gerry

Larry Leibovitch

## Subject Categories

Other Physics | Quantum Physics

## Keywords

quantum information theory, quantum state discrimination, quantum retrodiction

## Abstract

The problem of discriminating between non-orthogonal states is one that has generated a lot of interest. This basic formalism is useful in many areas of quantum information. It serves as a fundamental basis for many quantum key distribution schemes, it functions as an integral part of other quantum algorithms, and it is useful in experimental settings where orthogonal states are not always possible to generate. Additionally, the discrimination problem reveals important fundamental properties, and is intrinsically related to entanglement. In this thesis, the focus is on exploring the problem of sequentially discriminating between non-orthogonal states. In the simplest version these schemes, Alice sends one of two known pure states to Bob who performs a non-optimal discrimination procedure such that the post measurement states resulting from his measurement can then be discriminated by a third participant, Charlie. In these schemes, the goal is to optimize the joint probability of both Bob and Charlie succeeding. In devising such a scheme, there are several different criteria that can be prioritized. The most basic scheme, referred to as Minimum Error (ME) discrimination, prioritizes Bob's and Charlie's abilities to successfully determine which state was sent by Alice. In this scheme, Bob and Charlie each set up two detectors and based on the result from the detector they make a guess as to which state was sent. For instance, if Bob registers a click in his first detector, he concludes that Alice sent the first state. As each detector has some probability to produce a result for either incoming result, Bob and Charlie optimize their joint probability of success by optimizing the probability that each detector will fire when the correlated state is sent by Alice. Another possible scheme, referred to as Unambiguous Discrimination (UD), prioritizes Bob's and Charlie's ability to correctly determine the state sent by Alice. In this scheme, Bob and Charlie each set up three detectors, where if a result is obtained from the first two detectors Bob or Charlie can determine with certainty which state was sent by Alice. One final setup, referred to as Discrimination with a Fixed Rate of Inconclusive Outcome, is a combination of the previous two schemes, where Bob and Charlie maximize their probability of successfully determining the state sent by Alice where they allow some fixed probability that they will not be able to determine which state Alice sent. This fixed inconclusive probability allows Bob and Charlie to control how much they prioritize correctly determining the state that was sent, as in the Unambiguous Discrimination, versus prioritizing successfully determining the state sent by Alice, as in Minimum Error discrimination. One final topic that will be discussed by this thesis is Quantum Retrodiction. Quantum Retrodiction applies an alternate perspective on the communication protocol between Alice and Bob. In the predictive model, Alice calculates the probability that Bob gets a specific measurement result given that she prepares her system in a specific state. In the retrodictive model, Bob calculates the probability that Alice prepared her system in a specific state given the result of his measurement. This alternate perspective on the communication procedure gives new a new understanding and new tools for approaching the problem of state discrimination, as exemplified by applying the retrodictive formalism to unambiguous discrimination.

## Recommended Citation

Fields, Dov L., "Sequential Discrimination Between Non-Orthogonal Quantum States" (2019). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/3326