Simulating Quantum Processes using Classical Structures : This book explains how category theory can be used to explain various phenomena in the realm of quantum mechanics and quantum computer-science

Manav Bhushan

ISBN 10: 3639345258 / ISBN 13: 9783639345254

Published by VDM Verlag Dr. Müller, 2011

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - In earlier work, it has been shown that Frobenius algebras with certain properties can be used to simulate classical data. They are especially useful because in their definition itself they incorporate the biggest difference between classical and quantum data- which is the absence of copying and deleting operations for arbitrary quantum states. In later work, it has been shown that a special, commutative, dagger-Frobenius algebra (classical structure) corresponds to an orthonormal basis for a finite- dimensional Hilbert Space. In this paper, we show how classical structures can be used to axiomatize maximally entangled states for two qubits. We then go on explain how this new representation of quantum informatic related protocols using classical structures can be used to encode the flow of quantum data. We explain how this process encodes all the possible observational branches simultaneously, and thus has the ability to tell us the end result that can be achieved in any particular protocol. We end with a summary of the results obtained, and suggestions for future work.

Seller Inventory # 9783639345254

Bibliographic Details

• Title: Simulating Quantum Processes using Classical Structures : This book explains how category theory can be used to explain various phenomena in the realm of quantum mechanics and quantum computer-science
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2011
• Language: English
• ISBN 10: 3639345258
• ISBN 13: 9783639345254
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 22W x 15H x 0.4D centimeters 22 centimeters width by 15 centimeters height by 0.4 centimeters depth
• Weight: 118 grams

About this title

Synopsis

In earlier work, it has been shown that Frobenius algebras with certain properties can be used to simulate classical data. They are especially useful because in their definition itself they incorporate the biggest difference between classical and quantum data- which is the absence of copying and deleting operations for arbitrary quantum states. In later work, it has been shown that a special, commutative, dagger-Frobenius algebra (classical structure) corresponds to an orthonormal basis for a finite- dimensional Hilbert Space. In this paper, we show how classical structures can be used to axiomatize maximally entangled states for two qubits. We then go on explain how this new representation of quantum informatic related protocols using classical structures can be used to encode the flow of quantum data. We explain how this process encodes all the possible observational branches simultaneously, and thus has the ability to tell us the end result that can be achieved in any particular protocol. We end with a summary of the results obtained, and suggestions for future work.

About the Author

The author is currently pursuing a PhD at the Engineering Science department in Oxford University.