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How to extract weak values from a mesoscopic electronic system

Iliya Esin, Alessandro Romito, Yuval Gefen

Published Sep 1, 2016• 2 citations
OpenAlex

Abstract

Weak value (WV) protocols may lead to extreme expectation values that are larger than the corresponding orthodox expectation values. Recent works have proposed to implement this concept in nano-scale electronic systems. Here we address the issue of how one calibrates the setup in question, maximizes the measurement's sensitivity, and extracts distinctly large WVs. Our concrete setup consists of two Mach-Zehnder interferometers (MZIs): the "system" and the "detector". Such setups have already been implemented in experiment.

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We propose and study a weak value (WV) protocol in the context of a solid state setup, specifically, an electronic Mach-Zehnder interferometer. This is the first specific proposal to measure both the real and imaginary part (i.e., complete tomography) of a WV. We also analyze the manifestation of many-body physics in the WV to be measured, including finite temperature and shot-noise-like contributions.

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Vaidmans nested MZI, again

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Weak values in continuous weak measurements of qubits

Lupei Qin, Pengfei Liang, Xin-Qi Li

For continuous weak measurements of qubits, we obtain exact expressions for weak values (WVs) from the postselection restricted average of measurement outputs, by using both the quantum-trajectory equation (QTE) and the quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the ``very'' weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert, and Vaidman (AAV), in the sense that our result incorporates nonperturbative correction which could be important when the AAV WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier's noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful results for homodyne measurement in a circuit-QED system, which allows for measuring the real and imaginary parts of the AAV WV by simply tuning the phase of the local oscillator. This advantage can be exploited as an efficient state-tomography technique.

Physical Review A•Jul 23, 2015•8 citations

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Throughout the "creation" of Quantum Mechanics, a theory has been built that is based on a single way of measuring quantum systems. These measurements have always taken place so that the act of measuring disturbs the system to the point of collapsing it, and then it acquires all the properties of a single state. However, in the late 1980s, a new way of measuring a quantum system emerged, called the Weak Measurement. With it, we were able to deal with experiments with a new approach, where the configuration of the measurement is changed by a factor that disturbs the system very little. With the way of measuring before this new concept, it would be impossible to detect small changes in a quantum system, but now, the weak measurement reaches new horizons. We developed a form of weak measurement using a general coupling in terms of the superposition of an initial state and a final state, in the case of a qubit. With that, it was possible to see in more detail how the process of this way of measuring occurs, where we will see how the coupling between the two states must be done to carry out such an experiment. We have also developed a weak measurement in a quantum system using a Mach-Zehnder interferometer for such a study. In it, with the help of a value that will determine how weak the weak measure is, we can carry out a measure in which we do not need to disturb a system to obtain information.

•Jul 27, 2020•0 citations

Weak values in continuous weak measurement of qubits

Lupei Qin, Liang, Pengfei, Xin-Qi Li

For continuous weak measurement of qubits, we obtain exact expressions for weak values (WVs) from the post-selection restricted average of measurement outputs, by using both the quantumtrajectory- equation (QTE) and quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the "very" weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert and Vaidman (AAV), in a sense that our result incorporates non-perturbative correction which could be important when the AAV's WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier's noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful result for homodyne measurement in circuit-QED system, which allows for measuring the real and imaginary parts of the AAV's WV by simply tuning the phase of the local oscillator. This advantage can be exploited as efficient state-tomography technique.

arXiv:1502.02396•Feb 9, 2015•0 citations
Weak value (WV) protocols may lead to extreme expectation values that are larger than the corresponding orthodox expectation values. Recent works have proposed to implement this concept in nano-scale electronic systems. Here we address the issue of how one calibrates the setup in question, maximizes the measurement's sensitivity, and extracts distinctly large WVs. Our concrete setup consists of two Mach-Zehnder interferometers (MZIs): the "system" and the "detector". Such setups have already been implemented in experiment.
For continuous weak measurements of qubits, we obtain exact expressions for weak values (WVs) from the postselection restricted average of measurement outputs, by using both the quantum-trajectory equation (QTE) and the quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the ``very'' weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert, and Vaidman (AAV), in the sense that our result incorporates nonperturbative correction which could be important when the AAV WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier's noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful results for homodyne measurement in a circuit-QED system, which allows for measuring the real and imaginary parts of the AAV WV by simply tuning the phase of the local oscillator. This advantage can be exploited as an efficient state-tomography technique.
Throughout the "creation" of Quantum Mechanics, a theory has been built that is based on a single way of measuring quantum systems. These measurements have always taken place so that the act of measuring disturbs the system to the point of collapsing it, and then it acquires all the properties of a single state. However, in the late 1980s, a new way of measuring a quantum system emerged, called the Weak Measurement. With it, we were able to deal with experiments with a new approach, where the configuration of the measurement is changed by a factor that disturbs the system very little. With the way of measuring before this new concept, it would be impossible to detect small changes in a quantum system, but now, the weak measurement reaches new horizons. We developed a form of weak measurement using a general coupling in terms of the superposition of an initial state and a final state, in the case of a qubit. With that, it was possible to see in more detail how the process of this way of measuring occurs, where we will see how the coupling between the two states must be done to carry out such an experiment. We have also developed a weak measurement in a quantum system using a Mach-Zehnder interferometer for such a study. In it, with the help of a value that will determine how weak the weak measure is, we can carry out a measure in which we do not need to disturb a system to obtain information.
For continuous weak measurement of qubits, we obtain exact expressions for weak values (WVs) from the post-selection restricted average of measurement outputs, by using both the quantumtrajectory- equation (QTE) and quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the "very" weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert and Vaidman (AAV), in a sense that our result incorporates non-perturbative correction which could be important when the AAV's WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier's noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful result for homodyne measurement in circuit-QED system, which allows for measuring the real and imaginary parts of the AAV's WV by simply tuning the phase of the local oscillator. This advantage can be exploited as efficient state-tomography technique.