Selective Quantum State Tomography
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be done with the following notable advantages (i) a number of state copies that depends only on the desired precision of the estimation, rather than the dimension of the unknown state; (ii) a similar reduction in the requisite classical memory and computational cost; (iii) a saturation of the known optimal bounds for full state tomography with independent measurements. As an immediate extension to this technique we show that SQST can be used to generate an universal data sample, of fixed and dimension independent size, from which one can extract the mean values of a continuous number of operators. We close by showing that our method saturates the optimal bound when applied to the recently posed problem of shadow tomography.
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Joshua Morris (add twitter)
Borivoje Dakić (add twitter)
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09/15/19 06:06PM
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