Artificial non-Gaussian operations and states for quantum information processing applications

Mgr. Jan PROVAZNÍK

Doctoral thesis

Artificial nonlinearity for quantum information processing applications

Abstract:

Quantum non-Gaussian operations are one of the essential ingredients needed for universal quantum computation with continuous-variable quantum states of light. The scarcity of naturally occurring non-Gaussian interactions can be compensated with suitable measurement-induced non-Gaussian operations. Their implementations still require high-quality quantum non-Gaussian states that can be manufactured artificially with various techniques of quantum state synthesis. Several original research papers are covered in this dissertation, starting with a proposal for improved single photon subtraction procedure which can be utilized within specific protocols for state synthesis and in entanglement distillation. Another avenue of research focuses on preparation of ancillary non-Gaussian states needed in measurement-induced cubic phase interaction and studies the effects of different photonic detectors on the quality of prepared physical approximations of cubic phase states. The analysis is complemented by a novel approach towards dealing with numerical issues inherent to numerical simulations of continuous-variable quantum systems. Quantum non-Gaussian states, despite their critical role in quantum computation and communication, are susceptible to loss. A particular decoherence mitigation strategy based on Gaussian operations is presented and investigated in the dissertation. Its effects against decoherence due to loss combined with thermal noise are discussed and analyzed for the family of quantum-optical Schrodinger states of light. % Quantum non-Gaussian Schrodinger states serve an important role in quantum computation and communication, however, their non-Gaussian features are susceptible to loss. In a further direction of research a particular mitigation strategy aiming to reduce their decoherence due to loss combined with thermal noise is discussed and analyzed. Ongoing research directions presented in the dissertation include an analysis of realistic experimental conditions required for synthesis of certifiable quantum states of four photons, and a novel algorithm with exponential improvement in computational complexity is introduced for calculation of a special qualitative measure of non-Gaussian resources, enabling its application in complex scenarios. The dissertation concludes with a brief incursion into the realm of genuine multi-partite entangled states. Certain classes of these states can be detected using optimal witnesses obtained with the aid of semi-definite programming. The pertinent semi-definite programs were implemented in collaboration with experimental group aiming to prepare and certify a special discrete-variable state of light with genuine multi-partite entanglement provable solely from its separable two-body marginals. In further theoretical collaboration similarly exotic states were discovered in the domain of continuous-variable light. These efforts eventually culminated in development of open-source software libraries presented within the dissertation.

Abstract:

Quantum non-Gaussian operations are one of the essential ingredients needed for universal quantum computation with continuous-variable quantum states of light. The scarcity of naturally occurring non-Gaussian interactions can be compensated with suitable measurement-induced non-Gaussian operations. Their implementations still require high-quality quantum non-Gaussian states that can be manufactured artificially with various techniques of quantum state synthesis. Several original research papers are covered in this dissertation, starting with a proposal for improved single photon subtraction procedure which can be utilized within specific protocols for state synthesis and in entanglement distillation. Another avenue of research focuses on preparation of ancillary non-Gaussian states needed in measurement-induced cubic phase interaction and studies the effects of different photonic detectors on the quality of prepared physical approximations of cubic phase states. The analysis is complemented by a novel approach towards dealing with numerical issues inherent to numerical simulations of continuous-variable quantum systems. Quantum non-Gaussian states, despite their critical role in quantum computation and communication, are susceptible to loss. A particular decoherence mitigation strategy based on Gaussian operations is presented and investigated in the dissertation. Its effects against decoherence due to loss combined with thermal noise are discussed and analyzed for the family of quantum-optical Schrodinger states of light. % Quantum non-Gaussian Schrodinger states serve an important role in quantum computation and communication, however, their non-Gaussian features are susceptible to loss. In a further direction of research a particular mitigation strategy aiming to reduce their decoherence due to loss combined with thermal noise is discussed and analyzed. Ongoing research directions presented in the dissertation include an analysis of realistic experimental conditions required for synthesis of certifiable quantum states of four photons, and a novel algorithm with exponential improvement in computational complexity is introduced for calculation of a special qualitative measure of non-Gaussian resources, enabling its application in complex scenarios. The dissertation concludes with a brief incursion into the realm of genuine multi-partite entangled states. Certain classes of these states can be detected using optimal witnesses obtained with the aid of semi-definite programming. The pertinent semi-definite programs were implemented in collaboration with experimental group aiming to prepare and certify a special discrete-variable state of light with genuine multi-partite entanglement provable solely from its separable two-body marginals. In further theoretical collaboration similarly exotic states were discovered in the domain of continuous-variable light. These efforts eventually culminated in development of open-source software libraries presented within the dissertation.

Keywords

quantum optics, quantum states of light, quantum information processing, quantum non-Gaussianity, continuous-variables, numerical simulation, numerical optimization, cubic phase states, decoherence mitigation, coherent Schrodinger states, Fock state capability, genuine multi-partite entanglement

Language used: English

Date on which the thesis was submitted / produced: 30. 8. 2024

Thesis defence

• Supervisor: doc. Mgr. Petr Marek, Ph.D., doc. Mgr. Petr Marek, Ph.D.

Palacký University Olomouc

Faculty of Science

Doctoral programme / field:
Physics / Optics and Optoelectronics