Abstract:The erasure of information is fundamentally an irreversible logical operation, carrying profound consequences for the energetics of computation and information processing. We investigate the thermodynamic costs associated with erasing (and preparing) quantum processes. Specifically, we analyze an arbitrary bipartite unitary gate acting on logical and ancillary input-output systems, where the ancillary input is always initialized in the ground state. We focus on the adversarial erasure cost of the reduced dynamics - that is, the minimal thermodynamic work cost to erase the logical output of the gate for any logical input, assuming full access to the ancilla but no access to any purifying reference of the logical input state. We determine that this adversarial erasure cost is directly proportional to the negative min-entropy of the reduced dynamics, thereby giving the dynamical min-entropy a clear operational meaning. The dynamical min-entropy can take positive and negative values, depending on the underlying quantum dynamics. The negative value of the erasure cost implies that the extraction of thermodynamic work is possible instead of its consumption during the process. A key foundation of this result is the quantum process decoupling theorem, which quantitatively relates the decoupling ability of a process with its min-entropy. This insight bridges thermodynamics, information theory, and the fundamental limits of quantum computation.
From: Himanshu Badhani [view email]
[v1]
Thu, 5 Jun 2025 17:53:17 UTC (321 KB)
[v2]
Thu, 24 Jul 2025 08:30:32 UTC (356 KB)
[v3]
Thu, 8 Jan 2026 08:37:51 UTC (348 KB)
[v4]
Thu, 22 Jan 2026 11:21:10 UTC (349 KB)
[v5]
Tue, 23 Jun 2026 16:18:58 UTC (348 KB)
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