Simplified Quantum Process Tomography

We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the incorporation of prior knowledge of the class of physical interactions involved in generating the dynamics, which reduces the problem to one of parameter estimation. This allows part of the problem to be tackled using efficient convex methods, which, when coupled with a constraint on some parameters allows globally optimal estimates for the Kraus operators to be determined from experimental data. Parameterising the maps provides further advantages: it allows the incorporation of mixed states of the environment as well as some initial correlation between the system and environment, both of which are common physical situations following excitation of the system away from thermal equilibrium. Although the approach is not universal, in cases where it is valid it returns a complete set of positive maps for the dynamical evolution of a quantum system at all times.Comment: Added references to interesting related work by Bendersky et a

Completely Positive Maps and Classical Correlations

We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord [H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)]. We prove that initial states that have only classical correlations lead to completely positive reduced dynamics. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We outline the implications of our results to quantum process tomography experiments.Comment: 4 pages, 1 figur

Quantum process tomography and Linblad estimation of a solid state qubit

We present an example of quantum process tomography (QPT) performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the chi matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al. [N. Boulant, T.F. Havel, M.A. Pravia and D.G. Cory, Phys. Rev. A 67, 042322 (2003)]