Abstract The uncertainty principle sets a bound on our ability to predict the measurement outcome of two incompatible observables precisely. The entropic uncertainty lower bound can be improved by considering an additional particle as the quantum memory B which has correlation with the measured particle A . Here, we consider the quantum memory-assisted entropic uncertainty for the case in which the quantum memory and the measured particle are topological qubits. In our scenario the topological quantum memory B interacts with environment. We will study Ohmic-like fermionic and bosonic environments. We also investigate the effect of the fermionic and bosonic environments on the lower bounds of the amount of the key which can be extracted per state by Alice and Bob for quantum key distribution protocols.

中文翻译：

---

环境下两个拓扑量子比特的量子记忆辅助熵不确定性和秘密率的下界

摘要 不确定性原理限制了我们精确预测两个不相容的观测值的测量结果的能力。熵不确定性下界可以通过考虑一个额外的粒子作为与被测粒子 A 相关的量子存储器 B 来改善。在这里，我们考虑量子存储器和被测粒子是拓扑量子位的情况下的量子存储器辅助熵不确定性。在我们的场景中，拓扑量子存储器 B 与环境相互作用。我们将研究类欧姆费米子和玻色子环境。我们还研究了费米子和玻色子环境对 Alice 和 Bob 可以为量子密钥分发协议按状态提取的密钥数量下限的影响。