اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHow to implement the generalized-coherent-state POVM via nonadaptive continuous isotropic measurement
51
0
0.0
(
0
)
تأليف
Chris S. Jackson
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In a recent Letter~[PRL textbf{121}, 130404 (2018)], it was announced that the spin-coherent-state POVM can be implemented via a nonadaptive continuous isotropic measurement. In this article, the mathematical concepts used to prove this are explained in greater depth. Also provided is the more general result of how to implement a generalized-coherent-state POVM for any finite-dimensional unitary representation of a Lie group.
قيم البحث
اقرأ أيضاً
Recently it was reported that the spin-coherent state (SCS) positive-operator-valued measure (POVM) can be performed for any spin system by continuous isotropic measurement of the three total spin components [E. Shojaee, C. S. Jackson, C. A. Riofrio,
A. Kalev, and I. H. Deutsch, Phys. Rev. Lett. 121, 130404 (2018)]. The outcome probability distribution of the SCS POVM for an input quantum state is the generalized $Q$-function, which is defined on the 2-sphere phase space of SCSs. This article develops the theoretical details of the continuous isotropic measurement and places it within the general context of applying curved-phase-space correspondences to quantum systems, indicating their experimental utility by explaining how to analyze this measurements performance. The analysis is in terms of the Kraus operators that develop over the course of a continuous isotropic measurement. The Kraus operators represent elements of the Lie group $mathrm{SL}(2,mathbb{C})$, a complex version of the usual unitary operators that represent elements of $mathrm{SU}(2)$. Consequently, the associated POVM elements represent points in the 3-hyperboloid $mathrm{SU}(2)backslashmathrm{SL}(2,mathbb{C})$. Three equivalent stochastic techniques, path integral, diffusion (Fokker-Planck) equation, and stochastic differential equations, are applied to show that the POVM quickly limits to the SCS POVM. We apply two basic mathematical tools to the Kraus operators, the Maurer-Cartan form, modified for stochastic applications, and the Cartan decomposition associated with the symmetric pair $mathrm{SU}(2)subsetmathrm{SL}(2,mathbb{C})$. Informed by these tools, the three stochastic techniques are applied directly to the Kraus operators in a representation independent, and thus geometric, way (independent of any spectral information about the spin components).
Generalized quantum measurements identifying non-orthogonal states without ambiguity often play an indispensable role in various quantum applications. For such unambiguous state discrimination scenario, we have a finite probability of obtaining incon
clusive results and minimizing the probability of inconclusive results is of particular importance. In this paper, we experimentally demonstrate an adaptive generalized measurement that can unambiguously discriminate the quaternary phase-shift-keying coherent states with a near-optimal performance. Our scheme is composed of displacement operations, single photon detections and adaptive control of the displacements dependent on a history of photon detection outcomes. Our experimental results show a clear improvement of both a probability of conclusive results and a ratio of erroneous decision caused by unavoidable experimental imperfections over conventional static generalized measurements.
We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum non-demolition. Despite several claims of ``measuring noncommuting observ
ables in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing or retrodiction. In particular, we examine proposals to estimate the result of an external measurement made on an open quantum systems during a period where it is also undergoing continuous monitoring. A full analysis shows that the non-demolition principle is not actually violated, and so a well-posed as a statistical inference problem can be formulated. We extend the formalism to consider multiple independent external measurements made on the system over the course of a continual period of monitoring.
Present protocols of criticality enhanced sensing with open quantum sensors assume direct measurement of the sensor and omit the radiation quanta emitted to the environment, thereby omitting potentially valuable information. Here we propose a protoco
l for criticality enhanced sensing via continuous observation of the emitted radiation quanta. Under general assumptions, we establish a scaling theory for the global quantum Fisher information of the joint system and environment state at a dissipative critical point. We demonstrate that it obeys universal scaling laws featuring transient and long-time behavior governed by the underlying critical exponents. Importantly, such scaling laws exceed the standard quantum limit and can in principle satuarate the Heisenberg limit. To harness such advantageous scaling, we propose a practical sensing scheme based on continuous detection of the emitted quanta. In such a scheme a single interrogation corresponds to a (stochastic) quantum trajectory of the open system evolving under the non-unitary dynamics dependent on the parameter to be sensed and the back-action of the continuous measurement. Remarkably, we demonstrate that the associated precision scaling significantly exceeds that based on direct measurement of the critical steady state, thereby establishing the metrological value of detection of the emitted quanta at dissipative criticality. We illustrate our protocol via counting the photons emitted by the open Rabi model, a paradigmatic model for the study of dissipative phase transition with finite components. Our protocol is applicable to diverse open quantum sensors permitting continuous readout, and may find applications at the frontier of quantum sensing such as human-machine interface, magnetic diagnosis of heart disease and zero-field nuclear magnetic resonance.
We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the paramete
r takes on a finite range of values. Leveraging recent convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
