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arXiv:2311.00303

Error-disturbance uncertainty relations in a superconducting quantum processor

TINGRUI DONG, So-Young Baek, Fumihiro Kaneda, Keiichi Edamatsu

Published Nov 1, 2023• 0 citations
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Abstract

We experimentally test the error-disturbance uncertainty relation (EDR) in generalized, variable strength measurements of superconducting qubits on a NISQ processor. Making use of sequential weak measurements that keeps the initial signal state practically unchanged prior to the main measurement, we demonstrate that the Heisenberg EDR is violated, yet the Ozawa and Branciard EDRs are valid throughout the range of measurement strengths from no measurement to projection measurement. Our results verify that universal EDRs are valid even in a noisy quantum processor and will stimulate research on measurement-based quantum information and communication protocols using a NISQ processor.

DOI
10.48550/arxiv.2311.00303

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Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.
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In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle inequalities. Several versions of universally valid error-disturbance relations (EDR) have already been obtained and experimentally verified in the regimes where naive applications of the Heisenberg uncertainty relation failed. However, these EDRs were formulated for discrete measurements. In this paper, we consider continuous measurement processes and obtain new EDR inequalities in the Fourier space: in terms of the power spectra of the system and probe variables. By applying our EDRs to a linear optomechanical system, we confirm that a tradeoff relation between error and disturbance leads to the existence of an optimal strength of the disturbance in a joint measurement. Interestingly, even with this optimal case, the inequality of the new EDR is not saturated because of doublely existing standard quantum limits in the inequality.