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Journal of Shaanxi Normal University

A brief introduction to discrimination and cloning of quantum states

Cao Huaixi

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In the classical information theory,coding state can be accurately copied and distinguished;while in quantum information,it is impossible to copy,delete and distinguish non-orthogonal states due to the superposition of states.However,discrimination and cloning of quantum states have extensive applications in the new-type quantum information science such as receiving and eavesdropping in the quantum cryptography and so on.In this review paper,the mathematical concepts and the related research results about discrimination and cloning of quantum states are briefly introduced.

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In the classical information theory,coding state can be accurately copied and distinguished;while in quantum information,it is impossible to copy,delete and distinguish non-orthogonal states due to the superposition of states.However,discrimination and cloning of quantum states have extensive applications in the new-type quantum information science such as receiving and eavesdropping in the quantum cryptography and so on.In this review paper,the mathematical concepts and the related research results about discrimination and cloning of quantum states are briefly introduced.
In quantum information processing and quantum computing protocols information is encoded in the state of a quantum system. After processing the information it has to be read out which is equivalent to determining the final state of the system. When the possible final states are not orthogonal this is a highly nontrivial task that constitutes the general area of what is known as quantum state discrimination. It consists in finding measurement schemes that, according to some figure of merit, will determine the state of the system. Optimized measurement schemes often lead to generalized measurements (Positive Operator Valued Measures, POVMs). In this tutorial review we begin with a brief introduction to the theory of generalized measurements and illustrate the power of the concept on examples relevant to applications in quantum cryptography.
In quantum information processing and quantum computing protocols the carrier of information is a quantum system and information is encoded in the state of a quantum system. After processing the information it has to be read out what is equivalent to determining the final state of the system. When the possible final states are not orthogonal this is a highly nontrivial task that constitutes the general area of what is known as quantum state discrimination. It consists in finding measurement schemes that, according to some figure of merit, will determine the state of the system. Optimized measurement schemes often lead to generalized measurements (Positive Operator Valued Measures [POVMs]). In this tutorial review we illustrate the power of the POVM concept on examples relevant to applications in quantum cryptography. In order to keep the flow of the presentation we give a brief introduction to the quantum theory of measurements, including generalized measurements (POVMs), in the Appendices.
This thesis is a study of how information theory can be used to analyse and interpret quantum mechanical systems, specifically, systems that are being used for information processing and communication tasks. Quantum information science is a relatively new field, and it has only been recently that we have started to look at using quantum mechanical systems to accomplish information processing tasks that are not possible using classical systems. As this method of information processing is a relatively new paradigm, there are many possibilities for new algorithms and discoveries in this area of computing. The application of information theory towards the analysis and description of quantum mechanical systems yields new interesting results - it can even be argued that information theory provides a natural and intuitive way to intepret quantum mechanics, as correlations and measurement outcomes in quantum processes can be described using information theory. Chapter 1 is an introduction to the strange new world of quantum mechanics and takes a brief look at one of the applications of quantum information science in quantum cryptography. A mathematical overview of the postulates and framework that quantum mechanics is built on is presented in Chapter 2. Chapter 3 is a brief study of classical information theory and some of the fundamental concepts and ideas that form the crux of the subject. In Chapter 4, we present the main results of the thesis by taking a look at an optimal measurement scheme that improves on previous schemes by allowing us to extract the maximal amount of information from states in a quantum channel of specific geometry. The findings have an impact on various other areas of the field, including security analysis of quantum cryptographic protocols and building better quantum cloning machines.
The impossibility of perfectly copying (or cloning) an unknown quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These ``quantum cloning machines'' are important tools for studying a wide variety of tasks, e.g., state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines both for discrete-dimensional and for continuous-variable quantum systems. In addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.
The no-cloning theorem has always been a hot topic in quantum theorem: As an impossibility result, this theorem precludes attempts to communicated faster than light and reinforces the security of several quantum cryptography protocol. In this survey, I will briefly introduce the history of quantum no-cloning theorem–how the thesis was invented, how did it get its name; And i would also discuss the hitherto progress on no-cloning theorem, several approach of none-perfect cloning on non-orthogonal states as well as the application of quantum no-cloning theorem in quantum cryptography and quantum information. This survey incorporates the lecture ”Quantum Information Amplifiers Beyond the No-Cloning Theorem” given by Prof. Giulio Chiribella and ”Quantum cryptography” given by Prof. Xiongfeng Ma.