Venegas-Li Ariadna E, Jurgens Alexandra M, Crutchfield James P
Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Phys Rev E. 2020 Oct;102(4-1):040102. doi: 10.1103/PhysRevE.102.040102.
When an experimentalist measures a time series of qubits, the outcomes constitute a classical stochastic process. We show that projective measurement induces high complexity in these processes in two specific senses: They are inherently random (finite Shannon entropy rate) and they require infinite memory for optimal prediction (divergent statistical complexity). We identify nonorthogonality of the quantum states as the mechanism underlying the resulting complexities and examine the influence that measurement choice has on the randomness and structure of measured qubit processes. We introduce quantitative measures of this complexity and provide efficient algorithms for their estimation.
当实验人员测量量子比特的时间序列时，测量结果构成一个经典随机过程。我们证明，投影测量在两个特定意义上会使这些过程产生高复杂性：它们本质上是随机的（有限的香农熵率），并且需要无限的记忆来进行最优预测（发散的统计复杂性）。我们将量子态的非正交性确定为产生这些复杂性的潜在机制，并研究测量选择对测量的量子比特过程的随机性和结构的影响。我们引入了这种复杂性的定量度量，并提供了有效的算法来进行估计。
