Entanglement Distillation - Motivation

Motivation

Suppose that two parties, Alice and Bob, would like to communicate classical information over a noisy quantum channel. Either classical or quantum information can be transmitted over a quantum channel by encoding the information in a quantum state. With this knowledge, Alice encodes the classical information that she intends to send to Bob in a (quantum) product state, as a tensor product of reduced density matrices .... where each is diagonal and can only be used as a one time input for a particular channel .

The fidelity of the noisy quantum channel is a measure of how closely the output of a quantum channel resembles the input, and is therefore a measure of how well a quantum channel preserves information. If a pure state is sent into a quantum channel emerges as the state represented by density matrix, the fidelity of transmission is defined as .

The problem that Alice and Bob now face is that quantum communication over large distances depends upon successful distribution of highly entangled quantum states, and due to unavoidable noise in quantum communication channels, the quality of entangled states generally decreases exponentially with channel length as a function of the fidelity of the channel. Entanglement distillation addresses this problem of maintaining a high degree of entanglement between distributed quantum states by transforming N copies of an arbitrary entangled state into approximately Bell pairs, using only local operations and classical communication. The objective is to share strongly correlated qubits between distant parties (Alice and Bob) in order to allow reliable quantum teleportation or quantum cryptography.