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01 June 2023 |
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Quantum Overlapping Tomography | | Jordan Cotler
; Frank Wilczek
; | | Date: |
7 Aug 2019 | | Abstract: | 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 $e^{mathcal{O}(k)} log(n)$ 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 | | Services: | Forum | Review | PDF | Favorites | |
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