dq.measurements_sse_to_sme

measurements_sse_to_sme(
    measurements: ArrayLike, tsave: ArrayLike, etas: ArrayLike, key: PRNGKeyArray
) -> Array

Post-process measurements from a diffusive SSE simulation to obtain measurements for a diffusive SME simulation.

The SME measurements are obtained from the SSE measurements by adding additional Gaussian noise.

Note

More precisely, the SME measurement record \(\dd Y\) for a specific jump operator is defined as follows from the SSE measurement record \(\dd \tilde Y\): $$ \dd Y = \sqrt{\eta}\,\dd \tilde Y + \sqrt{1-\eta}\,\dd W $$ where \(\dd W\) is another independent Wiener process sampled for the post-processing.

The SME time-averaged measurement \(I(t_n, t_{n+1})\) is then defined as follows from the SSE time-averaged measurements \(\tilde I(t_n, t_{n+1})\): $$ I(t_n, t_{n+1}) = \frac{1}{\Delta t_n}\int_{t_n}^{t_{n+1}} \dd Y(t) = \sqrt{\eta}\, \tilde I(t_n, t_{n+1}) + \sqrt{1-\eta}\,\frac{\Delta W}{\sqrt{\Delta t_n}}, $$ where \(\Delta t_n=t_{n+1}-t_n\) and \(\Delta W\sim \mathcal{N}(0, 1)\) is a standard Gaussian random variable.

Parameters:

• measurements –

  See result of dq.dssesolve().

• tsave –

  See dq.dssesolve().

• etas –

  See dq.dsmesolve().

• key –

  PRNG key used to sample the added noise for the post-processing.

Returns:

• (array of shape (...)) –

  SME measurements. The shape is the same as measurements, except that the dimension corresponding to the number of jump operators measured may be smaller, if the corresponding efficiency is null.