Abstract
We introduce the concept of pairwise tomography networks to characterise quantum properties in many-body systems and demonstrate an efficient protocol to measure them experimentally. Pairwise tomography networks are generators of multiplex networks where each layer represents the graph of a relevant quantifier such as, e.g., concurrence, quantum discord, purity, quantum mutual information, or classical correlations. We propose a measurement scheme to perform two-qubit tomography of all pairs showing exponential improvement in the number of qubits $N$ with respect to previously existing methods. We illustrate the usefulness of our approach by means of several examples revealing its potential impact to quantum computation, communication and simulation. We perform a proof-of-principle experiment demonstrating pairwise tomography networks of $W$ states on IBM Q devices.
Highlights
The identification, characterization, and measurement of quantum properties in complex many-body systems is one of the greatest challenges of modern quantum physics
We introduce the concept of pairwise tomography networks to characterize quantum properties in many-body systems and demonstrate an efficient protocol to measure them experimentally
The results presented in this article lay the foundations of a interdisciplinary framework combining concepts of complex network science, quantum information, quantum measurement theory, and condensed-matter physics
Summary
The identification, characterization, and measurement of quantum properties in complex many-body systems is one of the greatest challenges of modern quantum physics. We introduce the concept of quantum tomography multiplexes, i.e., multilayer networks where the nodes are the qubits and, in every layer, the weighted links represent some (classical or quantum) pairwise quantity that can be directly obtained from the tomographic data. This results in a single mathematical object containing information about pairwise entanglement, mutual information, classical correlations, von Neumann entropy, quantum discord, or any other two-body quantifier which might be useful to characterize both manybody states and real quantum devices. IV, we summarize our results and present conclusions and future perspectives
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