Abstract
Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [Á. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two- and four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures.
Highlights
Correlations play a central role in quantum physics
We investigate in detail the noise dynamics and its correlations for different physical encodings of the qubits that lead to different correlation characteristics
We study the dynamics of spatial correlations of noise processes in a trapped ion quantum information processor [51]
Summary
Correlations play a central role in quantum physics. A wide range of quantum effects including apparently disconnected topics, such as Bell inequalities or quantum phase transitions, can be analyzed by considering correlations. In order to assess whether or not these conditions are met in experimental quantum processors, theoretically well-founded and practically applicable methods to characterize the strength as well as the distance-dependence of spatial correlations are required Such tools become important in scalable quantum information processing architectures: There, it is forseeable that the noise environment will not be fully correlated in processors consisting of multiple smaller units that are interconnected by quantum channels. This law states that the amount of correlations of some given dynamics cannot increase by adding uncorrelated dynamics to it, i.e. a process for the quantifier equals zero This ordering property for the amount of dynamical correlations is analogous to the fundamental law in the resource theory of entanglement [1, 3].
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