Quantum Dense Coding

Keywords and Synonyms

Super dense coding ; Dense coding      

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 ${ | \psi \rangle }$ and row vectors are denoted as ${ | \psi \rangle^{\dagger} = {| \psi \rangle^*}^T \equiv \langle \psi | }$. The complex inner-product between vectors ${ | \psi \rangle }$ and ${ | \phi \rangle }$ is conveniently written as ${ \langle \psi | \phi \rangle }$.

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