My research is in quantum information processing, with a focus on the study of decoherence, inaccuracy and errors in quantum computation and communication. I am especially interested in:
- Quantum noise models
- Quantum computations in experimentally realistic conditions
- Quantum cryptography and communication protocols in experimentally realistic conditions and against quantum adversaries
- Quantum information representations
- Quantum channels capacities
- I aim at designing error models capable of describing all physically possible single-qubit and two-qubit errors, decoherence and noise effects.
- General error models are achieved by characterizing general transformations of single-qubit and two-qubit density matrices, and extension of the utilized methods to multi-qubit systems is indeed possible. Generality of error model is pursued in order to offer a complete, realistic and physically feasible description of the most general experimental situation which could happen in quantum computational or communication frameworks.
- Error models allow for the investigation of the qualitative behavior and noise tolerance of quantum algorithms and communication protocols. I have designed a general single-qubit error model and utilized it to test, for instance, an entanglement purification protocol for quantum cryptography and communication purposes, a quantum-Fourier-transform-based protocol for simulation of simple quantum systems, error correcting codes in presence of multiple errors. Different noise channels have proven to affect different quantum protocols very differently, and both the qualitative behavior and the noise tolerance of the protocols are affected to different extents. Thus, given a protocol and its experimental implementation, this allows for the identification of dangerous perturbations as well as the protocol's different sensitivities to noise.
- I also explore special cases of physically realistic errors in the main experimental implementations of universal two-qubit operations. Realistic perturbations affecting two-qubit operations can be modeled according to their experimental implementation, and the resulting error models can be applied to explore the impact of these experimentally-derived two-qubit imperfections on quantum computation and communication protocols.
- I design and explore novel graphical representations for quantum information.
- Aiming at understanding how the information contained in quantum states is manipulated by computations performed on multi-qubit systems, the graphical technique called "diagrams of states" allows for an alternative and often more useful approach to analyze in minute detail the functioning of known quantum algorithms, and an auxiliary tool to conceive novel quantum computations.
- Similarly to quantum circuits, diagrams of states are a space-time representation of quantum operations; horizontal lines represent states of the computational basis instead of qubits, and the action of quantum gates is graphically represented by the corresponding effects on the quantum states composing the system.
- This technique describes in a very intuitive and detailed way basic quantum features, protocols and computations. The graphic representations has so far been utilized to investigate, for instance, evolution of open quantum systems, single-qubit decoherence and noise transformations, the role of entanglement in quantum information, the action of quantum copying machines, the distinctive features of oracle- and query-based quantum algorithms, the action of error correcting codes. This technique is also employed in the study of two-qubit decoherence and general noise transformations.
- Quantum cryptography allows for secure communication by exploiting the properties of quantum information. Such communications, in theory completely secure, could be hacked in practical implementations by taking advantage of non-ideal behavior of the equipment and other kind of imperfections. In the Quantum Hacking group (UNIK University Graduate Center, Oslo, and NTNU, Trondheim), I studied how it is possible to prove security even in realistic conditions and to incorporate into security proofs the imperfections that cannot be eliminated from the system.
- In the Information Quantique team (Télécom ParisTech, Paris), I explored zero-error capacity of quantum channels, and quantum cryptographic primitives other than key distribution that could offer practical applications in the future secure communication systems. These research objectives were pursued in the context of the research projects QPRIM at Institut Télécom and COCQ at ANR, Paris.
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