Exclusive Control of Quantum Memory Erasure

Abstract

Erasing memory is a fundamental operational task in quantum information processing, governed by Landauer's principle, which links information loss to thermodynamic work. We introduce and analyze assisted quantum erasure, where correlations with a remote system reduce the energetic cost of resetting a memory. We identify exclusive control of erasure as the central operational requirement: only a designated party should be able to achieve the minimal cost, while any adversary necessarily fails. In the device-dependent regime, we show that entanglement of formation exactly characterizes exclusivity, establishing entanglement as the decisive thermodynamic resource. Moving to a one-sided device-independent scenario, in which only the memory holder's device is trusted, we develop an operational erasure protocol based on random dephasing and conditional operations. These results elevate quantum erasure from a thermodynamic constraint to an operational primitive: the erasure work cost quantifies secure, exclusive control over quantum memory, guaranteeing that an unauthorized agent cannot fully erase information under bounded work.

Figures (3)

• Figure 1: Illustration of assisted erasure with competing parties. Bob’s system, $\rho_B$, begins in a high-entropy state (red). Alice and Eve each hold systems correlated with Bob’s, and perform local measurements ($A_M$ and $E_{M}$) to assist in erasure. The resulting conditional states $\rho_{B|A_M}$ and $\rho_{B|E_M}$ show reduced entropy (blue and purple), reflecting Alice’s and Eve’s influence. Despite both parties having correlations with Bob, only Alice achieves complete erasure, reflecting a stronger correlation than Eve. The thermometer encodes the residual entropy of Bob’s memory, visually distinguishing exclusive thermodynamic control.
• Figure 2: One-sided semi-DI protocol: Bob’s random dephasing, Alice’s announcement, conditional erasure, and verification.
• Figure 3: Per–run work costs for assisted erasure on the two–qubit Werner state $\rho_W(p)$. The solid curve shows Alice's assisted cost in both DD and SDI scenarios $W_{A\to B}= \widetilde{W}_{A\to B}$, the dashed curve shows Eve's assisted cost $W_{E\to B}^{\mathrm{DD}}$ in the device–dependent scenario (given by the entanglement of formation), and the dotted horizontal line marks the one–sided device–independent LHS floor $\widetilde{W}_{E\to B}^{\mathrm{LHS}} = \tfrac{1}{2}$ arising from two mutually unbiased dephasings on Bob. Vertical lines indicate the known thresholds for entanglement ($p>1/3$), steering ($p>1/2$), and Bell nonlocality ($p>1/\sqrt{2}$) yang2021decompositions. The intersections $W_{A\to B}=W_{E\to B}^{\mathrm{DD}}$ and $W_{A\to B}=\tfrac{1}{2}$ (not explicitly labelled here) mark the onset of exclusive thermodynamic control in the device–dependent and semi–device–independent regimes, witnessing entanglement and steering, respectively.

Theorems & Definitions (17)

• Definition 1
• Lemma 1
• Theorem 1
• Theorem 2
• Lemma 2
• Theorem 3
• Theorem 4
• Theorem 5
• proof
• proof