Publication Date:
2016-12-06
Description:
We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a known time evolution for a desired period of time. Afterwards we perform a measurement with a fixed measurement setup. This procedure can then be repeated for other periods of time, the measurement setup however remains unaltered. Given an n -dimensional system with suitable unitary dynamics, we show that any two states can be discriminated by performing a measurement with a setup that has n outcomes at n + 1 points in time. Furthermore, we consider scenarios where prior information restricts the set of states to a subset of lower dimensionality. Given an n -dimensional system with suitable unitary dynamics and a semi-algebraic subset R of its state space, we show that any two states of the subset can be discriminated by performing a measurement with a setup that has n outcomes at l steps of the time evolution if ( n − 1 ) l ≥ 2 dim R . In addition, by going beyond unitary dynamics, we show that one can in fact reduce to a setup with the minimal number of two outcomes.
Print ISSN:
0022-2488
Electronic ISSN:
1089-7658
Topics:
Mathematics
,
Physics
