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The European Physical Journal Plus

Temperature estimation in a quantum spin bath through entangled and separable two-qubit probes

Lionel Tenemeza Kenfack, William Degaulle Waladi Gueagni, Martin Tchoffo, Lukong Cornelius Fai

Published Feb 1, 2021• 7 citations
Publisher
DOI
10.1140/epjp/s13360-021-01180-x

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Quantum probes, such as single- and two-qubit probes, can accurately measure the temperature of a bosonic bath. The current investigation assesses the precision of the temperature estimate by using quantum Fisher information and the accompanying quantum signal-to-noise ratio. Employing an ancilla as a mediator between the probe and the bath improves thermometric sensitivity by transmitting temperature information into the probe qubit's coherences. In addition, we analyze two interacting qubits that were initially entangled or separated as quantum probes for various environmental configurations. Our findings show that increased precision is gained when the probe approaches its steady state, which is determined by the coupling between the two qubits. Furthermore, we can obtain high-efficiency temperature estimation for any low temperature by changing the interaction between the two qubits. Published by the American Physical Society 2024
We study how a second qubit can improve the estimation of spin-environment parameters when only one of the two qubits is measured. Both qubits are coupled to a common spin bath through the exactly solvable central-spin model, in which populations and coherences both evolve. Because the bath operator coupled to the qubits commutes with the bath Hamiltonian, the environment induces no effective interaction between the qubits. Without initial correlations or direct inter-qubit coupling, the two-qubit probe therefore performs exactly like a single qubit. When initial system-environment correlations are included, preparing the second qubit reshapes the environment statistics in a parameter-dependent way, and the measured qubit reads out this imprint. This improves the quantum Fisher information (QFI) for the coupling strength by factors of 3-4 relative to a correlated single-qubit probe, and by more than an order of magnitude relative to an uncorrelated one. For temperature estimation, the improvement reaches a factor of about 8. A direct Ising coupling does not help by itself, but the advantage persists in its presence. We also derive the classical Fisher information for arbitrary projective measurements and identify the measurement that saturates the QFI, which in general lies out of the equatorial plane of the Bloch sphere.
We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if the two qubits are embedded in a common bath, whereas if the interaction time is not constrained, then coherence rather than entanglement is the key resource in quantum thermometry.