Superposition of causal order as a metrological resource for quantum\n thermometry

Abstract

We propose a novel approach to qubit thermometry using a quantum switch, that\nintroduces an indefinite causal order in the probe-bath interaction, to\nsignificantly enhance the thermometric precision. The resulting qubit probe\nshows improved precision in both low and high temperature regimes when compared\nto optimal qubit probes studied previously. It even performs better than a\nHarmonic oscillator probe, in spite of having only two energy levels rather\nthan an infinite number of energy levels as that in a harmonic oscillator. We\nthereby show unambiguously that quantum resources such as the quantum switch\ncan significantly improve equilibrium thermometry. We also derive a new form of\nthermodynamic uncertainty relation that is tighter and depends on the energy\ngap of the probe. The present work may pave the way for using indefinite causal\norder as a metrological resource.\n