Multiple Quantum Memory-Assisted Information Exclusion Principle

Yong Hui Yu

Jun Zhang, Kan He, Hao Zhang +1 more

We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds. The lower bound depends on the observables’ complementarity and the complementarity of uncertainty whilst the upper bound includes the complementarity of the observables, quantum discord, and quantum condition entropy. In quantum measurement processing, there exists a relationship between the complementarity of uncertainty and the complementarity of information. In addition, based on the information exclusion principle the complementarity of uncertainty and the shareability of quantum discord can exist as an essential factor to enhance the bounds of each other in the presence of quantum memory.

Jun Zhang, Yang Zhang, Chang‐shui Yu

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion principle for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki's bound entangled state are investigated in details.

Wolfgang Tittel, Mikael Afzelius, Nicolas Gisin +2 more

Mir Alimuddin, Nathan Shettell, Raja Yehia +2 more

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, whereas any adversary must fail. 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. Finally, in a fully device-independent setting, we show how Bell nonlocality and self-testing translate observed violations into lower bounds on any adversary's erasure capability, yielding a device-independent notion of exclusive thermodynamic control. Taken together, these results elevate quantum erasure from a thermodynamic constraint to an operational primitive: the erasure work cost quantifies secure, exclusive control over quantum memory, ensuring that an unauthorized agent cannot fully erase information under a bounded work budget.

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