Compressing Quantum Fisher Information

TL;DR

This paper introduces a method to compress quantum Fisher information from pure states into a single qubit with minimal classical communication, demonstrated experimentally with photonic systems.

Contribution

It presents a novel quantum Fisher information compression technique for pure states, including sequential implementation and experimental validation.

Findings

Quantum Fisher information can be compressed into a single qubit with logarithmic classical bits.

Sequential compression of multiple qubits is feasible and demonstrated experimentally.

Two strategies, using Type-I fusion and CNOT gates, effectively implement the compression.

Abstract

We show that the quantum Fisher information about any phase parameter encoded in a family of pure quantum states can be faithfully compressed into a single qubit, accompanied by a logarithmic amount of classical bits. When the phase is encoded into many identical copies of a qubit state on the equator of the Bloch sphere, we show that the compression can be implemented sequentially, by iteratively compressing pairs of qubits into a single qubit. We experimentally demonstrate this building block in a photonic setup, developing two alternative compression strategies, based on Type-I fusion gate and a postselected implementation of the CNOT gate.