We present a new method for quantum process tomography enabling the efficient estimation, with fixed precision, of any of the parameters characterizing a quantum channel. The estimation strategy depends upon the set of matrix elements one selects to estimate. Furthermore, we describe a way to efficiently gather all the information required to efficiently estimate any average survival probability of the channel (i.e., to measure any diagonal element of its chi matrix).

In this paper we describe in detail and generalize a method for quantum process tomography that was presented in [1]. The method enables the efficient estimation of any element of the χ-matrix of a quantum process. Such elements are estimated as averages over experimental outcomes with a precision that is fixed by the number of repetitions of the experiment. Resources required to implement it scale polynomically with the number of qubits of the system. The estimation of all diagonal elements of the χ-matrix can be efficiently done without any ancillary qubits. In turn, the estimation of all the off-diagonal elements requires an extra clean qubit. The key ideas of the method, that is based on efficient estimation by random sampling over a set of states forming a 2-design, are described in detail. Efficient methods for preparing and detecting such states are explicitly shown.

Several methods, known as quantum process tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present a new method for quantum process tomography. We describe a new algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.

Many experimental setups in quantum physics use pseudorandomness in places where the theory requires randomness. In this Letter we show that the use of pseudorandomness instead of proper randomness in quantum setups has potentially observable consequences. First, we present a new loophole for Bell-like experiments: if some of the parties choose their measurements pseudorandomly, then the computational resources of the local model have to be limited in order to have a proper observation of nonlocality. Second, we show that no amount of pseudorandomness is enough to produce a mixed state by computably choosing pure states from some basis.

CitationLopez, Cecilia C. et al. "Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies." Physical Review A 81.6 (2010): 062113.We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)] and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and López et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements, and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the χ -matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way. characterization in a quantum information setting, that is, when the scalability of the tomographic method matters.