Decomposable dynamics on matrix algebras

• URL: http://arxiv.org/abs/2411.01712v1
• Date: Sun, 03 Nov 2024 23:30:36 GMT
• Title: Decomposable dynamics on matrix algebras
• Authors: Katarzyna Siudzińska, Krzysztof Szczygielski,
• Abstract summary: We encode the decomposable divisibility into the positivity of time-dependent coefficients that multiply generators of D-divisible dynamical maps. This provides an analogy to the CP-divisibility property, which is equivalent to the positivity of decoherence rates that multiply Markovian semigroup generators.
• Score: 0.0
• License:
• Abstract: We explore a notion of decomposably divisible (D-divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56, 485202 (2023). Both necessary and sufficient conditions are presented for highly-symmetric qubit and qudit dynamical maps. Through a restructurization of the evolution generators, we encode the decomposable divisibility into the positivity of time-dependent coefficients that multiply generators of D-divisible dynamical maps. This provides an analogy to the CP-divisibility property, which is equivalent to the positivity of decoherence rates that multiply Markovian semigroup generators.

Related papers

• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Non-Markovian quantum dynamics from symmetric measurements [0.0]
  We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement.
  arXiv  Detail & Related papers  (2024-02-06T21:26:22Z)
• Kac-Moody symmetries in one-dimensional bosonic systems [19.707384009550843]
  In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. We extend the lattice construction of the Kac-Moody generators to continuous systems and apply it to one-dimensional continuous boson systems.
  arXiv  Detail & Related papers  (2023-04-02T19:52:37Z)
• D-divisible quantum evolution families [0.0]
  We propose and explore a notion of decomposably divisible (D-divisible) differentiable quantum evolution families on matrix algebras. Necessary and sufficient conditions for D-divisibility are found.
  arXiv  Detail & Related papers  (2023-03-07T22:06:14Z)
• On Quantum Complexity [0.0]
  We consider a certain quantity as a possible candidate for quantum complexity. For explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.
  arXiv  Detail & Related papers  (2022-09-29T11:19:23Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Quasi-symmetry groups and many-body scar dynamics [13.95461883391858]
  In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When the group is a Lie group, an external field coupled to certain generators of the quasi-symmetry group lifts the degeneracy. We provide two related schemes for constructing one-dimensional spin models having on-demand quasi-symmetry groups.
  arXiv  Detail & Related papers  (2020-07-20T18:05:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.