Papers › Quantum Overlapping Tomography
Quantum Overlapping Tomography
Jordan Cotler, Frank Wilczek
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It 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^(𝒪(k)) log²(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.
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