Quantum Dense Coding

Years and Authors of Summarized Original Work

• 1992; Bennett, Wiesner

Problem Definition

Quantum information theory distinguishes classical bits from quantum bits or qubits. The quantum state of n qubits is represented by a complex vector in $(\mathbb{C}^{2})^{\otimes n}$, where $(\mathbb{C}^{2})^{\otimes n}$ is the tensor product of n 2-dimensional complex vector spaces. Classical n-bit strings form a basis for the vector space $(\mathbb{C}^{2})^{\otimes n}$. Column vectors in $(\mathbb{C}^{2})^{\otimes n}$ are denoted as $\vert \uppsi \rangle$ and row vectors are denoted as $\vert \uppsi \rangle ^{\dag } =\vert \uppsi \rangle ^{{\ast}T} \equiv \langle \uppsi \vert$. The complex inner product between vectors $\vert \uppsi \rangle$ and $\vert \upphi \rangle$ is conveniently written as $\langle \uppsi \vert \upphi \rangle$.

Entangled quantum states $\vert \psi \rangle \in (\mathbb{C}^{2})^{\otimes n}$are those quantum states that cannot be written as a product of...