Efficient compression of quantum information

TL;DR

This paper introduces a quantum compression scheme that transforms many identical qubits into a significantly smaller quantum state, enabling efficient storage and communication of quantum information.

Contribution

It presents an exact, efficient method to compress tensor product states of identical qubits into a logarithmically small number of qubits using quadratic quantum gates.

Findings

Achieves compression of N qubits into log(N) qubits with quadratic gate complexity

Potential applications in quantum memory storage and directional quantum communication

Provides a practical approach for efficient quantum information encoding

Abstract

We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform N identically prepared qubits into a state, which is nontrivial only on the first log(N+1) qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-effective method for such an encoding.