Dylan H. Mahler

Adaptive quantum state tomography improves accuracy quadratically

We introduce a simple protocol for adaptive quantum state tomography, which reduces the worst-case infidelity [1-F(ρ,ρ)] between the estimate and the true state from O(1/sqrt[N]) to O(1/N). It uses a single adaptation step and just one extra measurement setting. In a linear optical qubit experiment, we demonstrate a full order of magnitude reduction in infidelity (from 0.1% to 0.01%) for a modest number of samples (N ≈ 3 × 10(4)).

Scalable spatial superresolution using entangled photons

We demonstrate spatial super-resolution, performing an optical centroid measurement on 4-photon N00N states with a scalable 11-detector measurement. Our results show spatial super-resolution with exponentially better detection efficiency than any previous N00N-state experiment.

Experimental nonlocal and surreal Bohmian trajectories

Researchers reconstruct trajectories of two entangled photons showing the nonlocal and “surreal” nature of the trajectories in Bohmian mechanics. Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

Self-calibrating quantum state tomography

We introduce and experimentally demonstrate a technique for performing quantum state tomography (QST) on multiple-qubit states despite incomplete knowledge about the unitary operations used to change the measurement basis. Given unitary operations with unknown rotation angles, our method can be used to reconstruct the density matrix of the state up to local rotations as well as recover the magnitude of the unknown rotation angle. We demonstrate high-fidelity self-calibrating tomography on polarization-encoded one- and two-photon states. The unknown unitary operations are realized in two ways: using a birefringent polymer sheet—an inexpensive smartphone screen protector—or alternatively a liquid crystal wave plate with a tuneable retardance. We explore how our technique may be adapted for QST of systems such as biological molecules where the magnitude and orientation of the transition dipole moment is not known with high accuracy.

Characterizing an entangled-photon source with classical detectors and measurements

Entangled-photon pairs are essential for many applications in quantum computation and communication, and quantum state tomography (QST) is the universal tool to characterize such entangled-photon sources. In QST, very low-power signals must be measured with single-photon detectors and coincidence logic. Here, we experimentally implement a new protocol, “stimulated-emission tomography” (SET), allowing us to obtain the information provided by QST when the photon pairs are generated by parametric fluorescence. This approach exploits a stimulated process that results in a signal several orders of magnitude larger than in QST. In particular, we characterize the polarization state of photons that would be generated in spontaneous parametric downconversion using SET. We find that SET accurately predicts the purity and concurrence of the spontaneously generated photons in agreement with the results of QST. We expect that SET will be extremely useful to characterize entanglement sources based on parametric fluorescence, providing a fast and efficient technique to potentially replace or supplement QST.

Quantum Data Compression of a Qubit Ensemble

Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even todays limited quantum memories far more powerful than previously recognized.

Dynamical symmetry reduction and discrete tomography of a Ξ atom

When implemented using a reasonable Hamiltonian, the tomography of a three-level Ξ atom is complicated by the equidistant energy levels of the atom. This restricts the possible transformations to those in the SO(3) subgroup of SU(3). Although complete reconstruction is possible for a single Ξ atom using a continuous set of tomograms, the discrete optimal set of tomograms, related to mutually unbiased bases in dimension 3, are not accessible by time evolution. We discuss here the search for an optimal set of discrete basis states compatible with the reduced SO(3) symmetry of the system.

In praise of weakness

Quantum physics is being transformed by a radical new conceptual and experimental approach known as weak measurement that can do everything from tackling basic quantum mysteries to mapping the trajectories of photons in a Youngs double-slit experiment. Aephraim Steinberg, Amir Feizpour, Lee Rozema, Dylan Mahler and Alex Hayat unveil the power of this new technique.

su(1,1) intelligent states

We construct all the intelligent states of the non-compact generators of su(1, 1) for every positive discrete representation of this Lie algebra, and discuss some of the properties of these states.

A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers

We present the first silicon-integrated homodyne detector suitable for characterising quantum states of light travelling in a silicon waveguide. We report high-fidelity quantum state tomography of coherent states. The device was also used to generate random numbers at a speed of 1.2 Gbps.