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Register a new userQuantum polyspectra for modeling and evaluating quantum transport measurements: A unifying approach to the strong and weak measurement regime
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Quantum polyspectra of up to fourth order are introduced for modeling and evaluating quantum transport measurements offering a powerful alternative to methods of the traditional full counting statistics. Experimental time-traces of the occupation dynamics of a single quantum dot are evaluated via simultaneously fitting their 2nd-, 3rd-, and 4th-order spectra. The scheme recovers the same electron tunneling and spin relaxation rates as previously obtained from an analysis of the same data in terms of factorial cumulants of the full counting statistics and waiting-time distributions. Moreover, the evaluation of time-traces via quantum polyspectra is demonstrated to be feasible also in the weak measurement regime even when quantum jumps can no longer be identified from time-traces and methods related to the full counting statistics cease to be applicable. A numerical study of a double dot system shows strongly changing features in the quantum polyspectra for the transition from the weak measurement regime to the Zeno-regime where coherent tunneling dynamics is suppressed. Quantum polyspectra thus constitute a general unifying approach to the strong and weak regime of quantum measurements with possible applications in diverse fields as nano-electronics, circuit quantum electrodynamics, spin noise spectroscopy, or quantum optics.
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In addition to the well-known Landauer-Buttiker scattering theory and the nonequilibrium Greens function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.
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Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumanns projective strong measurement and Aharonovs weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped $40Ca^+$ ion system. The transition is realized by tuning the interaction strength between the ions internal electronic state and its vibrational motion, which play the roles of the measured system and the measuring pointer, respectively. By pre- and post-selecting the internal state, a pointer state composed of two of the ions motional wavepackets is obtained, and its central-position shift, which corresponds to the measurement outcome, demonstrates the transition from the weak-value asymptotes to the expected-value asymptotes. Quantitatively, the weak-to-strong measurement transition is characterized by a universal transition factor $e^{-Gamma^2}$, where $Gamma$ is a dimensionless parameter related to the system-apparatus coupling. This transition, which continuously connects weak measurements and strong measurements, may open new experimental possibilities to test quantum foundations and prompt us to re-examine and improve the measurement schemes of related quantum technologies.
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill~cite{huang2020predicting}, a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict $M$ different functions of a state with only $mathcal{O}(log_2 M)$ measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonian. We compare the strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measures each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.
Since the photon box gedanken experiments of several of the founding fathers of modern physics, considerable progress has been made in differentiating the quantum and classical worlds. In this pursuit, the cavity as an open quantum system has been indispensable. From the quantization of the atom and field within a superconducting cavity, a unique realm of EPR type entanglement has emerged. In this way, dynamical evolution of the system in the strong coupling regime is intimately tied with the coupling of an atom with a single resonant or non-resonant mode within the cavity. More specifically, the cavity can be prepared so that the atom is detected in a desired state. Here, the essentials of the strong coupling regime of Cavity Quantum Electrodynamics (QED) are reviewed for cavities tuned with a single atomic transition. A brief introduction of the systems is followed by an approach of the more striking effects, leading towards Ramsey Interferometry and Quantum Non-Demolition measurements as means for quantum gate protocol. Because the integrity of the atom and photon states is important for the advancement of quantum computation, a brief discussion of the decoherence problems is also presented. This document is meant to introduce the topic in a way that makes it easily accessible to those working in closely related areas of physics, and to highlight key applications and some basic questions concerning decoherence and the measurement problem.
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