dual_from_state¶

dual_from_state(povm: BasePOVM, state: SparsePauliOp | DensityMatrix | Statevector) → BaseDual[source]¶

Return the dual frame of povm based on the outcome distribution of a supplied state.

This methods constructs a joint dual frame where the alpha-parameters are set as the outcome probabilities of the supplied state. It can be shown that this is the dual frame minimizing the variance of the estimator (irrespective of the observable to estimate) if outcomes are sampled from this state.

Parameters:

povm (BasePOVM) – the POVM for which we want to build a dual frame.
state (SparsePauliOp | DensityMatrix | Statevector) – state from which to compute the outcome probabilities.

Raises:

NotImplementedError – if povm is not a povm_toolbox.quantum_info.product_povm.MultiQubitPOVM instance.

Return type:

BaseDual