Quantum Dense Coding

Abstract

Quantum information theory distinguishes classical bits from quantum bits or qubits. The quantum state of n qubits is represented by a complex vector in .C2/ n, where .C2/ n is the tensor product of n 2-dimensional complex vector spaces. Classical n-bit strings form a basis for the vector space .C2/ n. Column vectors in .C2/ n are denoted as j§i and row vectors are denoted as j§i D j§i T h§j. The complex inner product between vectors j§i and j¥i is conveniently written as h§j¥i. Entangled quantum states j i 2 .C2/ n are those quantum states that cannot be written as a product of some vectors j i i 2 C, that is, j i ¤ N i j i i. The Bell states are four orthogonal