We investigate the decoherence in a $\mathcal{PT}$ -symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing the $\mathcal{PT}$ -symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and initial correlations as we approach the transition point.We investigate the decoherence in a $\mathcal{PT}$-symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing the$\mathcal{PT}$-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and initial correlations as we approach the transition point.

arXiv:1712.02554Dec 7, 20170 citations

Decoherence in a PT -Symmetric Qubit

Junaid Majeed Bhat, Muzaffar Qadir Lone, Sanjoy Datta +2 more

We investigate the decoherence in a PT -symmetric qubit coupled with a bosonic bath. Using canonical transformations, we map the non-Hermitian Hamiltonian representing the PT-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from the real eigen spectrum to a complex eigen spectrum. Using a general class of spectral densities, the strong suppression of the decoherence is observed due to both vacuum and thermal fluctuations of the bath, and the initial correlations hold, as we approach the transition point.We investigate the decoherence in a PT -symmetric qubit coupled with a bosonic bath. Using canonical transformations, we map the non-Hermitian Hamiltonian representing the PT-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from the real eigen spectrum to a complex eigen spectrum. Using a general class of spectral densities, the strong suppression of the decoherence is observed due to both vacuum and thermal fluctuations of the bath, and the initial correlations hold, as we approach the transition point.

Ukrainian Journal of PhysicsApr 20, 20232 citations

Generalized quantum Markov states

博道大野

Jan 1, 20050 citations

Quantum transition probability in convex sets and self-dual cones

Gerd Niestegge

The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time, and most advanced results are due to Alfsen and Shultz. Here we present a more elementary approach with a more general structure for the observables, which focuses on the transition probability of the quantum logical atoms. The binary case gives rise to the generalized qubit models and was fully developed in a preceding paper. Here we consider any case with finite information capacity (binary means that the information capacity is 2). A novel geometric property that makes any compact convex set a matching state space is presented. Generally, the transition probability is not symmetric; if it is symmetric, we get an inner product and a self-dual cone. The emerging mathematical structure comes close to the Euclidean Jordan algebras and becomes a new mathematical model for a potential extension of quantum theory.The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time, and most advanced results are due to Alfsen and Shultz. Here we present a more elementary approach with a more general structure for the observables, which focuses on the transition probability of the quantum logical atoms. The binary case gives rise to the generalized qubit models and was fully developed in a preceding paper. Here we consider any case with finite information capacity (binary means that the information capacity is 2). A novel geometric property that makes any compact convex set a matching state space is presented. Generally, the transition probability is not symmetric; if it is symmetric, we get an inner product and a self-dual cone. The emerging mathematical structure comes close to the Euclidean Jordan algebras and becomes a new mathematical model for a potential extension of quantum theory.

arXiv:2312.13213Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesNov 1, 20241 citation

Decoherence in a

\mathcal{PT}

-symmetric qubit

We investigate the decoherence in a

\mathcal{PT}

-symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing the

\mathcal{PT}

-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and initial correlations as we approach the transition point.