Partial-Measurement Backaction and Nonclassical Weak Values in a Superconducting Circuit

Abstract

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality. DOI: 10.1103/PhysRevLett.111.090506 PACS numbers: 03.67.Lx, 42.50.Dv, 42.50.Pq, 85.25.Àj Quantum measurement involves a fundamental tradeoff between information gain and disturbance of the measured system that is traceable to uncertainty relations [1]. The backaction, or kickback, is a nonunitary process that depends on the measurement result and premeasurement system state. Thought experiments in the 1980s unveiled paradoxes [2][3][4] where the backaction of multiple measurements of one system puts quantum mechanics at odds with macrorealism (MAR) [2], a set of postulates distilling our common assumptions about the macroscopic world. Steady developments in the control of single quantum systems have opened the road to testing these paradoxes with photons [5-9], superconducting circuits [10], and semiconductor spins [11][12][13].The Leggett-Garg inequality (LGI), for example, investigates the impact of backaction on the correlations between sequential measurements of one system [2,14]. A violation of the inequality certifies the failure of MAR to describe the system behavior. Although the original test called for multiple configurations of pairs of strong measurements, a generalization of the LGI using partial measurements requires only one configuration [15,16]. The first demonstration of LGI violations, by PalaciosLaloy et al.[10], used continuous weak measurement of a superconducting qubit. Further demonstrations followed using discrete measurements in photonic [7,8] and semiconductor-spin [12] systems. A second paradox is the nonclassicality of weak values, i.e., averages of a partial measurement conditioned on the result of a subsequent projective measurement [3]. These values are termed nonclassical when they lie outside the eigenspectrum of the weak measurement observable. Williams and Jordan [17] predicted an intriguing correspondence between nonclassical weak values (NCWVs) and the violation of generalized LGIs, first observed by Goggin et al.[7] using a photonic system. Moving beyond fundamental investigation, the emergent field of quantum feedback control [18] balances the tradeoff between information gain and backaction. Applications requiring controllable measurement strength can be found in quantum error correction [19], qubit stabilization [20,21], and state discrimination [22]. A variable-strength meas...

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