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01 June 2023
  » arxiv » 1908.2754

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Quantum Overlapping Tomography
Jordan Cotler ; Frank Wilczek ;
Date 7 Aug 2019
AbstractIt is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of $n$ qubits, one requires an exponential number of measurements in $n$, which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all $k$-qubit reduced density matrices of an $n$ qubit state can be determined with at most $e^{mathcal{O}(k)} log(n)$ rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with current experiments, the entanglement between every pair of qubits in a system of 1000 qubits could be measured and completely characterized in a few days. This corresponds to completely characterizing entanglement of nearly half a million pairs of qubits.
Source arXiv, 1908.2754
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