Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States

TL;DR

This paper introduces efficient one-shot quantum compression protocols for ensembles of identical mixed states, achieving significant memory savings and practical implementation on quantum computers.

Contribution

It provides the first protocols that compress mixed state ensembles into logarithmic qubits with optimality and efficiency, highlighting a discontinuous reduction in required qubits with small errors.

Findings

Achieves $O(\log N)$ qubit encoding for mixed states

Discontinuous qubit reduction when allowing small errors

25% memory saving for qubit ensembles

Abstract

We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.