Introduction to Quantum Information Science (Graduate Texts by Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi, Gen

By Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi, Gen Kimura, Tomohiro Ogawa

This ebook provides the fundamentals of quantum info, e.g., starting place of quantum concept, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum blunders correction and quantum cryptography. the mandatory wisdom is barely effortless calculus and linear algebra. this manner the publication will be understood by means of undergraduate scholars. so that it will research quantum info, one often has to check the basis of quantum concept. This publication describes it from extra an operational standpoint that's appropriate for quantum details whereas conventional textbooks of quantum thought lack this perspective. the present booklet bases on Shor's set of rules, Grover's set of rules, Deutsch-Jozsa's set of rules as uncomplicated algorithms. to regard numerous themes in quantum info, this e-book covers numerous types of details amounts in quantum structures together with von Neumann entropy. the boundaries of numerous forms of quantum details processing are given. As very important quantum protocols,this booklet comprises quantum teleportation, quantum dense coding, quantum information compression. specifically conversion concept of entanglement through neighborhood operation and classical conversation are handled too. This concept offers the quantification of entanglement, which coincides with von Neumann entropy. the following half treats the quantum speculation checking out. The selection challenge of 2 applicants of the unknown kingdom are given. The asymptotic functionality of this challenge is characterised through info amounts. utilizing this end result, the optimum functionality of classical info transmission through noisy quantum channel is derived. Quantum info transmission through noisy quantum channel by way of quantum mistakes correction are mentioned too. in accordance with this subject, the safe quantum verbal exchange is defined. specifically, the quantification of quantum safeguard which has no longer been handled in present e-book is defined. This ebook treats quantum cryptography from a more effective point of view.

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It is easy to see that the number of division becomes O(2n/2 ) by this replacement. For the primality test, it is known that there is a polynomial-time algorithm (namely, an algorithm whose computation time is at most n c for some constant c independent of input length n), which is called the Agrawal-Kayal-Saxena primality test [1]. Can we further improve the algorithm? , that is, how long computation time we require for primality test at least? In the field of the theoretical computer science, it is one of important research issues to prove lower bounds of time complexity of problems, namely, statements how long computation time any algorithm requires to solve the problem.

In order to define the concept strictly, we need to define a mathematical model of algorithms, but we can roughly define the complexity of some problem as sufficient and necessary numbers of elementary operations for solving the problem. Since this concept is directly connected to computation time for solving the problem, it is also called time complexity. ) Precisely, the time complexity is one of complexity measures defined over a specific computational model called the Turing machine, and thus, for the circuit model to be discussed, we require another measure based on its elementary operations than the time complexity.

It is easy to see that the number of division becomes O(2n/2 ) by this replacement. For the primality test, it is known that there is a polynomial-time algorithm (namely, an algorithm whose computation time is at most n c for some constant c independent of input length n), which is called the Agrawal-Kayal-Saxena primality test [1]. Can we further improve the algorithm? , that is, how long computation time we require for primality test at least? In the field of the theoretical computer science, it is one of important research issues to prove lower bounds of time complexity of problems, namely, statements how long computation time any algorithm requires to solve the problem.

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