Quantum process tomography via completely positive and trace-preserving projection

We present an algorithm for projecting superoperators onto the set of completely positive, trace-preserving maps. When combined with gradient descent of a cost function, the procedure results in an algorithm for quantum process tomography: finding the quantum process that best fits a set of sufficient observations. We compare the performance of our algorithm to the diluted iterative algorithm as well as second-order solvers interfaced with the popular CVX package for MATLAB, and find it to be significantly faster and more accurate while guaranteeing a physical estimate.Comment: 13pp, 8 fig

A journey into the world of inverse problems in quantum mechanics

Technology has come a long way since the birth of quantum mechanics. The science has led to computers, and now, the scientists are pushing the fundamentals further to eventually be able to construct a quantum computer from the bottom up. Quantum tomography has a vital role in this ambitious endeavour: it’s the study of how one can retrieve the values describing a quantum state, like finding coordinates on a map for a given position. The challenge that the quantum tomographer faces lies in the shear number of these values, which grows exponentially with the components of quantum system. This is the curse of dimensionality and cannot be avoided with classical means. Therefore, the tomographer is forced to come up with algorithms that scale well with the number of components, either via prior information or by reducing the problem to its simplest form. In this thesis, we devise algorithms for retrieving quantum states using a little of both approaches. We develop a direct way of retrieving quantum state-vector values by assuming that the state is pure, which is often the case in optics. In addition, we show that a simple optimisation technique, projected gradient descent, can outperform all other methods for retrieving general quantum states. Our contribution to the field is thus to provide tools that enable the tomographer to work on larger quantum states and that hopefully help her create the building blocks of a quantum computer. We touch on other somewhat related subjects such as image denoising and imaging quantum correlations

Acquisition of multiple photon pairs with an EMCCD camera

The detection and characterization of quantum states of light plays an important role in quantum science. Traditional methods use single-photon detectors, but these are generally limited to point measurements; consequently, multi-pixel devices are now being utilized in quantum measurements, especially in the field of quantum imaging. Here, we demonstrate the capability of an EMCCD camera to record multiple coincidence events originating from parametric downconversion where the mean photon number per pixel is much greater than unity. The multi-pixel nature of the camera enables us to record correlations ranging from $\approx 1$ to 10 000 coincidences per frame. This approach to quantum measurements provide mechanisms for recording quantum signatures for bright correlated photon sources

Discriminating single-photon states unambiguously in high dimensions

The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of unambiguous state discrimination (USD) enables error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between non-orthogonal, high-dimensional states encoded in single photons; our results range from dimension $d=2$ to $d=14$. We quantify the performance of our method by comparing the total measured error rate to the theoretical rate predicted by minimum-error state discrimination. For the chosen states, we find a lower error rate by more than one standard deviation for dimensions up to $d=12$. This method will find immediate application in high-dimensional implementations of quantum information protocols, such as quantum cryptography.Comment: 4 pages + 3 pages supplementary, 4 figure

A "fair sampling" perspective on an apparent violation of duality

In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited". [M. O. Scully, B.-G. Englert, and H. Walther. Nature, 351:111-116, 1991.] emphasized the importance of additional degrees of freedom in the context of complementarity. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work contributes to the explanation of previous experimental apparent violations of duality [R. Menzel, D. Puhlmann, A. Heuer, and W. P. Schleich. Proc. Natl. Acad. Sci., 109(24):9314-9319, 2012.] and opens up the way for novel experimental tests of duality.Comment: 10 pages, 8 figure

Nonlinear Optics: The Enabling Technology for Quantum Information Science

Nonlinear optical processes such as parametric down conversion and squeezed light generation are key elements of most quantum protocols, leading to crucial applications such as quantum imaging, sub-shot-noise metrology, and secure communication