Quantum Change

Charlotte D. Shelton

Kenji Nakahira

The identification of environmental changes is crucial in many fields. The present research is aimed at investigating the optimal performance for detecting change points in a quantum system when its Hamiltonian suddenly changes at a specific time. Assume that the Hamiltonians before and after the change are known and that the prior probability of each prospective change point is identical. These Hamiltonians can be time-dependent. The problem considered in this study is an extension of the problem of discriminating multiple quantum processes that consist of sequences of quantum channels. Although it is often extremely difficult to find an analytical solution to such a problem, we demonstrate that the maximum success probability for the Hamiltonian change point problem can be determined analytically and has a simple form.

Bai, Mei, Xiang-Yu Qin, Xue‐Qun Yan

We study the peculiar dynamics of two qubits quantum discord with a sudden change in behavior. It is widely agreed in the literature nowadays that environment induce sudden change behavior of quantum discord. We explore the sudden change phenomenon under the action of local-independent environments, considering the discord of two-qubit which is obtained by means of the weak measurements on one of the two-qubit. It is shown that the sudden change phenomenon does not appear under weak measurements. We find that the quantum discord with weak measurements decays in a monotonic fashion, and show that quantum discord might exhibit a sudden change only for the strong (projective) measurement. We believe that environment is not the main role of the sudden change, but the quantum correlation itself is.

Rachida Aïssaoui, John Amis

David Finkelstein

Bai, Ge, Francesco Buscemi, Valerio Scarani

Bayes’ rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimum change principle and use it to derive a quantum Bayes’ rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case, where Bayes’ rule is obtained by minimizing several distances between the joint input-output distributions. When the change maximizes the fidelity, the quantum minimum change principle has a unique solution, and the resulting quantum Bayes’ rule recovers the Petz transpose map in many cases.