Correlations, as intrinsic and intriguing features of quantum systems, have profound implications and applications in quantum information theory. Although substantial progress has been made in understanding and applying spatial correlations (i.e., those across different spatial systems at the same instant of time), temporal correlations (which emerge from the dynamics of a single quantum system across different instants of time) have been relatively less investigated. In this work, we first provide an axiomatic approach to temporal correlations by postulating natural requirements for a reasonable monotone of temporal correlations generated by a quantum channel. Then we study the temporal correlating power of quantum channels in terms of the Jordan product of quantum channels and compare it with the recently introduced notion of state over time. We introduce an information-theoretic monotone of such a power by exploiting the Jordan negativity and reveal its basic properties such as convexity, monotonicity, and unitary invariance. We further illustrate the monotone through several important channels and explicitly evaluate the corresponding temporal correlating power.

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• Quantum channels
• Quantum correlations in quantum information
• Quantum information theory