From the Heisenberg to the Schr\"{o}dinger Picture: Quantum Stochastic Processes and Process Tensors

• URL: http://arxiv.org/abs/2109.09256v3
• Date: Thu, 30 Sep 2021 06:56:00 GMT
• Title: From the Heisenberg to the Schr\"{o}dinger Picture: Quantum Stochastic Processes and Process Tensors
• Authors: Hendra I. Nurdin and John E. Gough
• Abstract summary: A general theory of quantum processes was formulated by Accardi, Frigerio and Lewis in 1982. This paper gives an exposition of quantum processes and the process tensor formalism to the quantum theory of probabilistic quantum processes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A general theory of quantum stochastic processes was formulated by Accardi, Frigerio and Lewis in 1982 within the operator-algebraic framework of quantum probability theory, as a non-commutative extension of the Kolmogorovian classical stochastic processes. More recently, studies on non-Markovian quantum processes have led to the discrete-time process tensor formalism in the Schr\"{o}dinger picture to describe the outcomes of sequential interventions on open quantum systems. However, there has been no treatment of the relationship of the process tensor formalism to the quantum probabilistic theory of quantum stochastic processes. This paper gives an exposition of quantum stochastic processes and the process tensor and the relationship between them. In particular, it is shown how the latter emerges from the former via extended correlation kernels incorporating ancillas.

Related papers

• Symmetry operations and Critical Behaviour in Classical to Quantum Stochastic Processes [0.0]
  We generate a large class of self contained quantum extensions by operations. We show that the relaxation processes for different quantum extensions are different and that is supported by the measure of coherence.
  arXiv  Detail & Related papers  (2024-09-14T03:01:54Z)
• Dilation theorem via Schr\"odingerisation, with applications to the quantum simulation of differential equations [29.171574903651283]
  Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. In this study, we demonstrate the viability of the recently devised Schr"odingerisation approach.
  arXiv  Detail & Related papers  (2023-09-28T08:55:43Z)
• Classicality from Quantum Stochastic Processes [0.0]
  I develop a theory of classicality from quantum systems. I present a characterization of channels in terms of their fixed points for the separable case. A quantum simulation of a polyhedral cone can then be constructed.
  arXiv  Detail & Related papers  (2023-07-09T20:07:28Z)
• Law of large numbers and central limit theorem for ergodic quantum processes [0.0]
  A discrete quantum process is represented by a sequence of quantum operations. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise.
  arXiv  Detail & Related papers  (2023-03-15T23:49:56Z)
• A Quantum-Classical Model of Brain Dynamics [62.997667081978825]
  Mixed Weyl symbol is used to describe brain processes at the microscopic level. Electromagnetic fields and phonon modes involved in the processes are treated either classically or semi-classically. Zero-point quantum effects can be incorporated into numerical simulations by controlling the temperature of each field mode.
  arXiv  Detail & Related papers  (2023-01-17T15:16:21Z)
• Memory Complexity of Quantum Processes [0.0]
  Generic open quantum dynamics can be described by two seemingly very distinct approaches. The process tensor framework describes all the possible observations one could possibly make on a quantum system. The intimate connection between quantum processes and classical processes is drawn in the end.
  arXiv  Detail & Related papers  (2022-03-03T03:04:33Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories [0.0]
  We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like variables. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system.
  arXiv  Detail & Related papers  (2020-03-18T18:32:47Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.