Problems and Solutions in Quantum Computing and Quantum InformationQuantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. The possibilities of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as to research workers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr Hamilton operator are included. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems |
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Alice and Bob apply arbitrary B₁ basis in C2 beam splitter Bell basis Bose annihilation operators Bose operators cloning coherent commutation relation complex numbers corresponding cos² decomposition defined denotes density matrix density operator described eigenstates eigenvalues eigenvectors equation finite-dimensional Hilbert spaces follows function given H₁ Hamilton operator hermitian Hilbert space identity operator linear operator log2 matrix representation measurement mode n×n matrix normalized eigenvectors obtain orthogonal orthonormal basis p₁ parameter particle Pauli matrices Pauli spin matrices phase photon polarization probability Problem 12 quantum computing qubit scalar product Show sin² Solution 11 space C2 space H standard basis U₁ UCNOT unit matrix unitary matrix unitary operator unitary transformation UNOT vector von Neumann entropy θλή μα σα ΣΣ στ συ