Coherence thermometry using multipartite quantum systems

Abstract

We investigate, how finite temperature influences quantum coherence in multipartite open systems by analyzing a tripartite spin boson model subjected to non-Markovian dephasing. Two distinct environmental configurations are considered viz. independent local reservoir and a common structured reservoir characterized by an Ohmic spectral density. In this framework, temperature enters explicitly through the time dependent dephasing rates, enabling a systematic exploration of thermal effects on coherence dynamics. Using the relative entropy of coherence, we examine representative pure states belonging to inequivalent entanglement classes along with physically relevant mixed states constructed from them. Under local non-Markovian dephasing, all states exhibit monotonic coherence decay, with temperature acting as a universal accelerator of decoherence. In contrast, the common reservoir scenario reveals a strikingly non-universal behaviour. While $GHZ$ and $Star$ type states undergo temperature enhanced degradation, $W$ class states and certain Werner type mixtures display robust stationary coherence that remains largely insensitive to thermal fluctuations. These results demonstrate that the thermal susceptibility of coherence is governed not only by environmental configuration but also by the internal architecture of multipartite quantum states. The interplay between reservoir structure and state geometry leads to qualitatively distinct dynamical regimes ranging from rapid thermal fragility to temperature resilient coherence preservation. Our findings identify coherence dynamics as a sensitive probe of structured finite temperature environments and suggest a pathway toward coherence based quantum thermometry and nanoscale calorimetry using engineered multipartite states.

Figures (5)

• Figure 1: Schematic illustration of a tripartite qubit system subjected to (a) local dephasing and (b) common dephasing environments. In the local configuration, each qubit interacts independently with its own bosonic bath (represented by three squares in fig. (a)) while the spheres are representing the qubits, leading to uncorrelated dephasing. In contrast, in the common environment, all qubits are collectively coupled to a single bosonic reservoir (single square in fig. (b)), giving rise to correlated dephasing dynamics. In both cases, the environments are assumed to be at finite temperature.
• Figure 2: The dynamics of coherence of pure states in a non-Markovian local environment. Here (a) represents the relative entropy of coherence $C_R(\rho)$ for the $GHZ$ state with dephasing strength parameter $kT = 0.1,~0.2,~0.5,~2,~10$; (b) shows the relative entropy of coherence $C_R(\rho)$ for the $Star$ state with same dephasing strength parameter while Figs. (c) and (d) are showing dynamics of $C_R(\rho)$ for $W$ state and $W \overline{W}$ state respectively.
• Figure 3: The dynamics of coherence of pure states in a non-Markovian common dephasing environment. Here (a) represents the relative entropy of coherence $C_R(\rho)$ for the $GHZ$ state with dephasing strength parameter $kT = 0.1,~0.2,~0.5,~2,~10$; (b) shows the relative entropy of coherence $C_R(\rho)$ for the $Star$ state with same dephasing strength parameter while Figs. (c) and (d) are showing dynamics of $C_R(\rho)$ for $W$ state and $W \overline{W}$ state respectively.
• Figure 4: The dynamics of coherence of mixed states in a non-Markovian local environment. Here (a)-(c) represent the relative entropy of coherence $C_R(\rho)$ of the mixed state $\rho_{GHZ}^{W}$ for mixing parameter $p=0.1$, $p=0.5$ and $p=0.9$ respectively, with dephasing strength parameters $kT = 0.1,~0.2,~0.5,~2,~10$; (d)-(f) show the relative entropy of coherence $C_R(\rho)$ for the mixed state $\rho_{WER}^{GHZ}$ with the same mixing parameters and dephasing strength parameters, while Figs. (g)-(i) show the dynamics of $C_R(\rho)$ for the mixed state $\rho_{WER}^{W}$ respectively.
• Figure 5: The dynamics of coherence of mixed states in a non-Markovian common environment. Here Figs. (a)-(c) represents the relative entropy of coherence $C_R(\rho)$ of the mixed state $\rho_{GHZ}^{W}$ for mixing parameter $p=0.1$, $p=0.5$ and $p=0.9$ respectively, with dephasing strength parameters $kT = 0.1,~0.2,~0.5,~2,~10$; Figs. (d)-(f) shows the relative entropy of coherence $C_R(\rho)$ for the mixed state $\rho_{WER}^{GHZ}$ with the same mixing parameters and dephasing strength parameters, while Figs. (g)-(i) are showing dynamics of $C_R(\rho)$ for mixed state $\rho_{WER}^{W}$ respectively.