Related papers: Precision measurement for open systems by non-hermitian linear response

Precision measurement for open systems by non-hermitian linear response

URL: http://arxiv.org/abs/2406.11287v2
Date: Sat, 28 Sep 2024 09:09:38 GMT
Title: Precision measurement for open systems by non-hermitian linear response
Authors: Peng Xu, Gang Chen,
Abstract summary: We first derive some general results regarding the lower bound of estimated precision for a dissipative parameter. This lower bound is related to the correlation of the encoding dissipative operator and the evolution time.
Score: 9.087477434347218
License:
Abstract: The lower bound of estimated precision for a coherent parameter unitarily encoded in closed systems has been obtained, and such a lower bound is inversely proportional to the fluctuation of the encoding operator. In this paper, we first derive some general results regarding the lower bound of estimated precision for a dissipative parameter, which is non-unitarily encoded in open systems, by combining the law of error propagation and the non-hermitian linear response theory. This lower bound is related to the correlation of the encoding dissipative operator and the evolution time. We next demonstrate the utility of our general results by considering three different kinds of non-unitary encoding processes, including particle loss, relaxation, and dephasing. We finally compare the lower bound with the quantum Fisher information obtained by tomography and find they are consistent in the regime where the non-hermitian linear response applies. This lower bound can guide us to find the optimal initial states and detecting operators to significantly simplify the measurement process.

Related papers

Error Feedback under $(L_0,L_1)$-Smoothness: Normalization and Momentum [56.37522020675243]
We provide the first proof of convergence for normalized error feedback algorithms across a wide range of machine learning problems. We show that due to their larger allowable stepsizes, our new normalized error feedback algorithms outperform their non-normalized counterparts on various tasks.
arXiv Detail & Related papers (2024-10-22T10:19:27Z)
Moment expansion method for composite open quantum systems including a damped oscillator mode [0.0]
We develop a numerical method to compute the reduced density matrix of the target system and the low-order moments of the quadrature operators. The application to an optomechanical setting shows that the new method can compute the correlation functions accurately with a significant reduction in the computational cost.
arXiv Detail & Related papers (2023-11-10T15:29:34Z)
Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer [30.920908325825668]
This paper presents a novel loss function to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing matrix problem solver.
arXiv Detail & Related papers (2023-10-07T09:47:55Z)
The Inductive Bias of Flatness Regularization for Deep Matrix Factorization [58.851514333119255]
This work takes the first step toward understanding the inductive bias of the minimum trace of the Hessian solutions in deep linear networks. We show that for all depth greater than one, with the standard Isometry Property (RIP) on the measurements, minimizing the trace of Hessian is approximately equivalent to minimizing the Schatten 1-norm of the corresponding end-to-end matrix parameters.
arXiv Detail & Related papers (2023-06-22T23:14:57Z)
Structural aspects of FRG in quantum tunnelling computations [68.8204255655161]
We probe both the unidimensional quartic harmonic oscillator and the double well potential. Two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi) are studied.
arXiv Detail & Related papers (2022-06-14T15:23:25Z)
System Identification via Nuclear Norm Regularization [44.9687872697492]
This paper studies the problem of identifying low-order linear systems via Hankel nuclear norm regularization. We provide novel statistical analysis for this regularization and carefully contrast it with the unregularized ordinary least-squares (OLS) estimator.
arXiv Detail & Related papers (2022-03-30T20:56:27Z)
Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
arXiv Detail & Related papers (2020-07-16T13:27:47Z)
One-Bit Compressed Sensing via One-Shot Hard Thresholding [7.594050968868919]
A problem of 1-bit compressed sensing is to estimate a sparse signal from a few binary measurements. We present a novel and concise analysis that moves away from the widely used non-constrained notion of width.
arXiv Detail & Related papers (2020-07-07T17:28:03Z)
Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment [52.02794488304448]
We propose a new distribution alignment method based on a log-likelihood ratio statistic and normalizing flows. We experimentally verify that minimizing the resulting objective results in domain alignment that preserves the local structure of input domains.
arXiv Detail & Related papers (2020-03-26T22:10:04Z)
Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors [52.06292503723978]
Motivated by advances in compressive sensing with generative models, we study the problem of 1-bit compressive sensing with generative models. We first consider noiseless 1-bit measurements, and provide sample complexity bounds for approximate recovery under i.i.d.Gaussian measurements. We demonstrate that the Binary $epsilon$-Stable Embedding property, which characterizes the robustness of the reconstruction to measurement errors and noise, also holds for 1-bit compressive sensing with Lipschitz continuous generative models.
arXiv Detail & Related papers (2020-02-05T09:44:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.