Decoherence and localization in open systems

Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound states of a two-mode open quantum system are investigated. The conditions for the emergence of dissipationless localized bound states are analytically solved, and the corresponding critical system-environment couplings under different values of the inter-mode coupling and the detuning are determined. The decoherence dynamics of the system under such conditions are analyzed and dissipationless coherence between the different localized bound states against decoherence is clearly shown. This may provide a new avenue to develop dissipationless quantum technology for quantum operations.Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound states of a two-mode open quantum system are investigated. The conditions for the emergence of dissipationless localized bound states are analytically solved, and the corresponding critical system-environment couplings under different values of the inter-mode coupling and the detuning are determined. The decoherence dynamics of the system under such conditions are analyzed and dissipationless coherence between the different localized bound states against decoherence is clearly shown. This may provide a new avenue to develop dissipationless quantum technology for quantum operations.

arXiv:2410.20840Oct 28, 20240 citations

Dynamical Localization and Decoherence

Farhan Saif, K. Riedel, W. P. Schleich +1 more

Springer eBooksNov 14, 20071 citation

On the Complexity of Finding Decoherence Free Subspaces

Evan Borras

Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the $k$ -Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality $k \geq 5$ , with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the $k$-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality $k \geq 5$, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.

quant-pharXiv:2609.26769Sep 23, 20260 citations

Decoherence: A Closed-System Approach

Sebastian Fortin, Olimpia Lombardi, Mario Castagnino

arXiv:1402.3525Brazilian Journal of PhysicsAug 19, 201329 citations

Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems

Irene Ada Picatoste, Alessandra Colla, Heinz‐Peter Breuer

We study the nonequilibrium thermodynamics of pure decoherence processes in open quantum systems coupled to a thermal reservoir. We review various definitions of central quantities, such as internal energy, work, heat, and entropy production, developed within local and global approaches to quantum thermodynamics. Within local approaches, thermodynamic quantities only refer to the open system's degrees of freedom, while in the global approaches, certain quantities are defined by referring explicitly to the reservoir degrees of freedom. Employing a microscopic, analytically solvable model, we perform a comparison of these two perspectives, revealing substantial differences in the thermodynamic quantities and in the formulations of the first and second laws. The main reason for these discrepancies is the fact that the global approaches involve the system-reservoir interaction which exchanges a large amount of energy with the environment, while the average open system energy is constant in time because the dynamics represents pure decoherence and does not affect the open system populations.We study the nonequilibrium thermodynamics of pure decoherence processes in open quantum systems coupled to a thermal reservoir. We review various definitions of central quantities, such as internal energy, work, heat, and entropy production, developed within local and global approaches to quantum thermodynamics. Within local approaches, thermodynamic quantities only refer to the open system's degrees of freedom, while in the global approaches, certain quantities are defined by referring explicitly to the reservoir degrees of freedom. Employing a microscopic, analytically solvable model, we perform a comparison of these two perspectives, revealing substantial differences in the thermodynamic quantities and in the formulations of the first and second laws. The main reason for these discrepancies is the fact that the global approaches involve the system-reservoir interaction which exchanges a large amount of energy with the environment, while the average open system energy is constant in time because the dynamics represents pure decoherence and does not affect the open system populations.

arXiv:2506.11633Physical Review AJul 23, 20254 citations

Open Quantum Systems and Decoherence

Kalle‐Antti Suominen

Springer eBooksJan 1, 20142 citations

k

-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality

k \geq 5

, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.