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arXiv:2307.08648 · Physical Review A

Compression of metrological quantum information in the presence of noise

Flavio Salvati, Wilfred Salmon, C. H. W. Barnes, David R. M. Arvidsson-Shukur

Published Aug 15, 2024• 5 citations
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Abstract

In quantum metrology, information about unknown parameters θ = ( θ 1 , ... , θ M ) is accessed by measuring probe states ρ ̂ θ . In experimental settings where copies of ρ ̂ θ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high postprocessing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in ρ ̂ θ ⊗ n into m < n copies of a postselected state: ρ ̂ θ ps ⊗ m . Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for m / n arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise. Published by the American Physical Society 2024

DOI
10.1103/physreva.110.022426

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In quantum metrology, information about unknown parameters θ = ( θ 1 , ... , θ M ) is accessed by measuring probe states ρ ̂ θ . In experimental settings where copies of ρ ̂ θ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high postprocessing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in ρ ̂ θ ⊗ n into m < n copies of a postselected state: ρ ̂ θ ps ⊗ m . Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for m / n arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise. Published by the American Physical Society 2024
The postselected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this Letter, we put forward a general theory on the compression channels in postselected quantum metrology. We define the basic notions characterizing the compression quality and illuminate the underlying structure of lossless compression channels. Previous experiments on postselected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory. Furthermore, 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. These findings can be employed to distribute quantum measurements so that the measurement noise and cost are dramatically reduced.
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Postselection can compress the metrological information and improve sensitivity in the presence of certain types of technical noise. Postselected quantum metrology with pure states has been significantly advanced recently. However, extending this framework to mixed states leads to formidable challenges, such as the difficulty in searching for lossless postselection measurements or even the loss of metrological information. In this work, we leverage the intuition for the lossless postselection of pure states and generalize the theory to the lossless postselection of a class of mixed states, dubbed quasi-pure states. We illustrate our findings in postselected quantum imaging, unitary estimation problems, and show that the quasi-pure structure can be universally engineered through only classical correlation with an ancilla. Our findings extend the utility of postselection techniques to scenarios with decoherence and also offer new perspectives to foundational questions in quantum information geometry.
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As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100× , respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024
Using quantum measurements to extract information from states is a matter of routine in quantum science and technologies. A recent work [Phys. Rev. Lett. 133, 040202 (2024)] reported the finding that the symmetric structures of a state can be harnessed to dramatically reduce the sample complexity in extracting information from the state. However, due to the presence of noise, the actual state at hand is often corrupted, making its symmetric structures distorted before the execution of quantum measurements. Here, using the methodology of quantum metrology, we identify the optimal measurement that can retrieve maximum information of a symmetric state from its corrupted copies. We show that this measurement can be found by solving a semidefinite program in generic cases and can be explicitly determined for a large class of noise models covariant under the symmetry group in question. The results of this study nicely complement the recent work by providing a method to optimally utilize the distorted symmetric structures of corrupted states for information retrieval.