Thermodynamic advancement in the causally inseparable occurrence of thermal maps

Tamal Guha, Mir Alimuddin, and Preeti Parashar

Phys. Rev. A 102, 032215 – Published 15 September 2020

Abstract

Quantum mechanics allows the occurrence of events without having any definite causal order. We show that the application of two different thermal channels in causally inseparable order can enhance the potential to extract work, in contrast to any of their definite order of occurrence. Surprisingly, this enhancement is possible even without assigning any thermodynamic resource value to the input qubits. Further, we provide a nontrivial example of causal enhancement using nonunital pin maps, the realization of which, in the superposition of path framework, has not been clearly known. Hence, our result may be a potential candidate to accentuate the difference between superposition of time and superposition of paths frameworks.

Received 24 March 2020
Accepted 13 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.032215

Physics Subject Headings (PhySH)

Quantum thermodynamics

Quantum Information, Science & TechnologyStatistical Physics & Thermodynamics

Authors & Affiliations

Tamal Guha^*, Mir Alimuddin^†, and Preeti Parashar^‡

Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India

^*g.tamal91@gmail.com
^†aliphy80@gmail.com
^‡parashar@isical.ac.in

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Issue

Vol. 102, Iss. 3 — September 2020

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Images

Figure 1
(a) No activation of free energy in the final state (depicted as a battery) for the definite causal order of occurrence of the thermal channels $N_{G A D}$ and $N_{P F}$ . (b) However, the same is activated when these channels appear in an indefinite causal order.
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Figure 2
The channel parameter is chosen as $p = q = 0.8$ and input state probability $r = 0.5 + 0.01 s$ , as mentioned earlier. The dashed blue curves stand for the causally inseparable order of occurrence, whereas the solid red curves stand for the causally separable cases. (a) Fixed bath scenario: The final free energy with respect to the input state parameter is plotted using a resourceful controller qubit. (b) Varying bath scenario: The free-energy difference between the final output and the initial state is plotted with the same controller.
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Figure 3
The channel parameter is chosen as $p = q = 0.8$ and input state probability $r = 0.5 + 0.01 s$ , as mentioned earlier. (a) Fixed bath scenario: The solid blue straight line at the bottom denotes the free energy of the final output under the causally separable combination of the channels $N_{P F}$ and $N_{G A D}$ , whereas the dashed yellow line stands for the final free energy under a causally inseparable combination of these two channels using the free thermal state as the controlling qubit. (b) Varying bath scenario: The solid red curve denotes the free-energy difference between the final output (under the causally separable combination of the channels) and the initial state. The dashed blue line stands for the same under a causally inseparable combination of these two channels with a thermal controller.
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Figure 4
Thermodynamic advancement using resource in the controller qubit. The yellow (lower) region denotes the variation of the final free energy under a causally separable order of occurrence for $N_{G A D}$ and $N_{P F}$ , and the blue (upper) region stands for their inseparable causal combination. The phase-flip parameter $q$ is chosen as 0.3. In (a), the final free energy is calculated with respect to the bath fixed by the $N_{G A D}$ channel parameter $p$ , whereas in (b), the same is calculated by assuming that the receiver has an access to the same bath as that of the input qubit.
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Figure 5
Thermodynamic advancement using resource-free controller qubit. The phase-flip parameter $q$ is chosen, as earlier. (a) The variation of the final free energy for a causally definite sequence of these two channels is depicted by the yellow (lower) region, whereas the blue (upper) region stands for a causally inseparable order of occurrence. (b) Here, the green (lighter) region depicts the causally inseparable case and the red (darker) region depicts the causally separable case.
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