Efficient Compression Channels for Post-selected Quantum Metrology

Core Concepts

A general theory on the compression channels in post-selected quantum metrology is proposed, which unifies weak-value amplification, post-selected metrology, and standard metrology. The necessary and sufficient conditions for lossless compression channels are derived, and examples with negligible loss are constructed.

Abstract

The content presents a comprehensive theory on compression channels in post-selected quantum metrology. The key highlights are:

The author defines the basic notions characterizing the compression quality, such as compression loss, compression capacity, and compression gain.

The author derives the necessary and sufficient conditions for lossless compression channels (LCCs) in post-selected quantum metrology, generalizing the optimal measurement conditions from standard quantum metrology.

The author shows that the structure of LCCs can be expressed in a generic form, where the POVM operators in the retained set are composed of a projector onto the orthogonal complement of the parameter-dependent state and a gauge operator.

The author demonstrates that for two categories of bipartite entangled states, the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem.

The author shows that previous experiments on post-selected optical phase estimation and weak-value amplification are particular cases of this general theory.

The author discusses how the results can be employed to distribute quantum measurements to dramatically reduce the measurement noise and cost.

Stats

Iω(σSA
x ) = Icl
ω
p(ω|x)

p(ω|x)I(σx|ω)
Iω(σSA
x ) ≤ Iω(ρx)

Quotes

"Post-selected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments."
"Previous experiments on post-selected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory."
"For two categories of bipartite systems, we show that the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem."

Key Insights Distilled From

Theory of Compression Channels for Post-selected Quantum Metrology

by Jing Yang at arxiv.org 04-11-2024

https://arxiv.org/pdf/2311.06679.pdf

Deeper Inquiries

How can the proposed theory on lossless compression channels be extended to mixed states or multi-parameter quantum states

The proposed theory on lossless compression channels can be extended to mixed states by considering the generalization of the compression channels for density matrices that are not pure states. In the case of mixed states, the QFI can be calculated using the quantum Cramér-Rao bound for mixed states, and the saturation conditions for the various bounds of the QFI need to be adapted to account for the mixed nature of the states. The compression channels for mixed states would involve optimizing the post-selection measurements to retain the maximum information about the parameter of interest while discarding the least informative components of the state. The extension to multi-parameter quantum states would involve considering the joint estimation of multiple parameters and designing compression channels that can efficiently extract information about all the parameters simultaneously.

What are the potential practical applications of the lossless compression channels beyond quantum metrology, such as in quantum sensing or quantum communication

The potential practical applications of lossless compression channels extend beyond quantum metrology to various areas in quantum technology. In quantum sensing, these compression channels can be utilized to reduce the number of samples required for high-precision measurements, leading to more efficient sensing protocols. In quantum communication, lossless compression channels can be employed to enhance the transmission of quantum information by reducing the amount of data that needs to be transmitted while maintaining the precision of the encoded information. Additionally, in quantum imaging and interferometry, these compression channels can help improve the resolution and sensitivity of imaging systems by optimizing the post-selection measurements to retain the most relevant information.

Can the compression channels be further optimized to achieve the ultimate precision limit in quantum metrology, even in the presence of various experimental imperfections

The compression channels can be further optimized to achieve the ultimate precision limit in quantum metrology by fine-tuning the post-selection measurements and the structure of the compression channels. By carefully designing the post-selection operators and the gauge operators in the compression channels, it is possible to minimize the loss of information during the compression process and maximize the retention of the quantum Fisher information. Additionally, advanced optimization techniques, such as adaptive estimation strategies and feedback control mechanisms, can be integrated into the compression channels to adaptively adjust the measurements based on the experimental conditions and improve the overall precision of the quantum metrological scheme. By continuously refining the compression channels and incorporating innovative strategies, it is feasible to approach the ultimate precision limit in quantum metrology even in the presence of experimental imperfections.