Thermal States in Quantum Information

Chakraborty, Anish (2023) Thermal States in Quantum Information. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Anish Chakraborty (18MS085)) Thesis_18MS085.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

Quantum mechanics, governed by unitary dynamics, is fundamentally reversible. This makes it both curious and surprising to consider thermal states within the quantum formalism, as these are equilibrium states by definition. In this work, we delve into the various ways thermal states appear in quantum information science. We explore the concept of thermal states as maximally entropic states, minimal free energy states, and completely passive states. We also examine the processes of equilibration and thermalization that lead to the emergence of typical states. Later in the thesis, we investigate the connection between thermal states and Werner states, demonstrating that for an n-dimensional system with only two energy levels, thermal states are always Werner-type states. We derive thresholds for temperature corresponding to various degrees of correlation, including entanglement, discord, and steerability, along with violation of Bell’s inequality. Finally, we study the manifestation of thermal states in spin chains and explore the relationship between quantum correlations and quantum phase transitions.

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