Measurement Induced Synthesis of Energy and Quantum Coherence

Mariia GUMBERIDZE

Doctoral thesis

Optical tests of quantum thermodynamics

Abstract:

Quantum coherence, stemming from the possibility of state superpositions in a quantum realm, has been extensively studied in the last decade. Inspired by the breakthrough of quantum batteries, in this thesis we present our idea of coherent charging of a quantum system. In distinction to the unitary transformations mainly used in the relevant literature for this purpose, we contribute to the variety by the usage of different types of quantum operations, namely, measurements. In this thesis, we study complementary values of energy and coherence of the specific system manipulated by the means of quantum measurements. Our system consists of many copies of independent two-level systems (TLS) with initial non-zero but small energy and coherence values. The goal is to increase its coherent energy. We show two methods of enhancement and simultaneous concentration of both quantities with the help of the measurement procedure. The originality of such an approach lies in the admission of much a broader class of transformations of completely positive (CP) maps compared to unitary operators, corresponding to completely positive trace-preserving maps (CPTP), used before. In addition, we explore the value of mutual coherence distinguishing the local and global contributions to the overall coherence of the system. Two approaches considered in the thesis are based on global (acting on all TLS) and pairwise (acting on pairs of TLS) measurements. The first one has a large probability of success whereas the second is presumably advantageous in more feasible experimental realization. The procedure was optimized with the introduction of the projective operator valued measures and tested for decoherence-induced imperfections. An experiment based on the idea of the thesis was conveyed independently by exploiting a photon-based setup with quantum filters and the results show to agree with the corresponding theoretical findings.

Abstract:

Quantum coherence, stemming from the possibility of state superpositions in a quantum realm, has been extensively studied in the last decade. Inspired by the breakthrough of quantum batteries, in this thesis we present our idea of coherent charging of a quantum system. In distinction to the unitary transformations mainly used in the relevant literature for this purpose, we contribute to the variety by the usage of different types of quantum operations, namely, measurements. In this thesis, we study complementary values of energy and coherence of the specific system manipulated by the means of quantum measurements. Our system consists of many copies of independent two-level systems (TLS) with initial non-zero but small energy and coherence values. The goal is to increase its coherent energy. We show two methods of enhancement and simultaneous concentration of both quantities with the help of the measurement procedure. The originality of such an approach lies in the admission of much a broader class of transformations of completely positive (CP) maps compared to unitary operators, corresponding to completely positive trace-preserving maps (CPTP), used before. In addition, we explore the value of mutual coherence distinguishing the local and global contributions to the overall coherence of the system. Two approaches considered in the thesis are based on global (acting on all TLS) and pairwise (acting on pairs of TLS) measurements. The first one has a large probability of success whereas the second is presumably advantageous in more feasible experimental realization. The procedure was optimized with the introduction of the projective operator valued measures and tested for decoherence-induced imperfections. An experiment based on the idea of the thesis was conveyed independently by exploiting a photon-based setup with quantum filters and the results show to agree with the corresponding theoretical findings.

Keywords

quantum thermodynamics, energy, relative entropy of coherence, mutual coherence, two-level systems

Language used: English

Date on which the thesis was submitted / produced: 13. 6. 2022

Thesis defence

• Supervisor: prof. Mgr. Radim Filip, Ph.D.

Palacký University Olomouc

Faculty of Science

Doctoral programme / field:
Physics / Optics and Optoelectronics