My PhD and post-doctoral research have focused on fully exploiting the multi-mode nature of a photon for the field of quantum information. I have specific expertise in high-dimensional quantum states of light—from their generation and control, to their precise measurement and application in a broad range of quantum imaging and communication protocols. Below, I summarize my main research contributions thus far.
1. High-dimensional quantum states of light: generation, measurement, and control
As part of my PhD thesis, I helped pioneer a high-dimensional quantum state (qudit) sorter that acts as a beam splitter for single photons carrying orbital angular momentum . Using this device, I implemented a new method for efficiently measuring large quantum states that used weak measurements for quantum tomography . In parallel, I helped develop a method for the rapid generation of photonic qudits using a digital micro-mirror device (DMD) that improved on existing speeds by two orders of magnitude . My more recent work has focused on developing methods for the precise manipulation of high-dimensional quantum states, such as a high-dimensional entanglement router  and cyclic transformations for photonic qudits .
2. Multi-photon entanglement in high dimensions
My post-doctoral research has concentrated on combining my knowledge of high-dimensional quantum information with the field of multi-photon entanglement. In a recent experiment, I created the first three-photon state entangled in a high-dimensional Hilbert space . This state exhibited a previously unobserved asymmetric entanglement structure, with two particles entangled in more levels than the third. In addition, I helped develop an algorithm that found quantum experiments for creating a vast family of new, high-dimensional multi-photon entangled states . Currently, I am in the final stages of an experiment where we are implementing one of these experiments to demonstrate violations of local-realism with a three-dimensional Greenberger-Horne-Zeilinger (GHZ) state .
3. Multi-level quantum communication through turbulence
Combining the generation and measurement techniques developed during my PhD, I demonstrated a lab-scale high-dimensional QKD protocol that used twisted light for encoding information . I have extensively studied the evolution of high-dimensional quantum states in strongly scattering turbulence [10, 11], with specific application towards performing high-dimensional QKD through the atmosphere. My research work in Vienna has built on this effort by establishing multi-level communication links over large scale distances, and showing their feasibility for macroscopic quantum entanglement experiments. Together with my colleagues, I demonstrated communication links with spatial modes of light over 3km in Vienna  and very recently, over a record distance of 143km in the Canary Islands .
4. Quantum-enhanced imaging
In addition to quantum cryptography, my PhD research has had a parallel focus on the use of quantum states of light for quantum-enhanced imaging and metrology. I developed a new type of quantum-secured imaging protocol which borrowed principles from QKD to provide security in an active imaging system . I also demonstrated a holographic quantum ghost-imaging technique that used a hologram as an image sorter for efficiently identifying an object . Along with my colleagues, I developed a compressive sensing-based object-tracking protocol that used entangled photons to efficiently track a moving object . In addition, I helped design an enhanced quantum phase estimation technique using N00N states that combined quantum and classical advantages .
 M. Mirhosseini, M. Malik, Z. Shi & R. W. Boyd, Nature Commun. 4:2781 (2013)
 M. Malik et al., Nature Commun. 5:3115 (2014)
 M. Mirhosseini et al., Opt. Exp. 21, 30204–30211 (2013)
 M. Erhard, M. Malik & A. Zeilinger, arXiv: 1605.05947 (2016)
 F. Schlederer, M. Krenn, R. Fickler, M. Malik & A. Zeilinger, New J. Phys. 18, 043019 (2016)
 M. Malik et al., Nat. Photonics 10, 248 (2016)
 M. Krenn, M. Malik, R. Fickler, R. Lapkiewicz & A. Zeilinger, Phys. Rev. Lett. 116, 090405 (2016)
 M. Erhard, M. Malik, M. Huber, M. Krenn & A. Zeilinger, In preparation (2016)
 M. Mirhosseini et al., New J. Phys. 17, 033033 (2015)
 M. Malik et al., Opt. Exp. 20, 13195–13200 (2012)
 B. Rodenburg et al., New J. Phys. 16, 033020 (2014)
 M. Krenn et al., New J. Phys. 16, 113028 (2014)
 M. Krenn et al., PNAS, doi:10.1073/pnas.1612023113 (2016)
 M. Malik, O. S. Magaña-Loaiza & R. W. Boyd, Appl. Phys. Lett. 101, 241103 (2012)
 M. Malik, H. Shin, M. N. O’Sullivan, P. Zerom & R. W. Boyd, Phys. Rev. Lett. 104, 163602 (2010)
 O. S. Magaña-Loaiza, M. Malik, G. A. Howland, J. C. Howell & R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013)
 H. Shin, O. S. Magaña-Loaiza, M. Malik, M. N. O’Sullivan & R. W. Boyd, Opt. Exp. 21, 2816 (2013).