Open quantum systems are harder to track than open classical systems

@article{Warszawski2019OpenQS,
  title={Open quantum systems are harder to track than open classical systems},
  author={Prahlad Warszawski and Howard M. Wiseman},
  journal={Quantum},
  year={2019}
}
For a Markovian (in the strongest sense) open quantum system it is possible, by continuously monitoring the environment, to perfectly track the system; that is, to know the stochastically evolving pure state of the system without altering the master equation. In general, even for a system with a finite Hilbert space dimension D, the pure state trajectory will explore an infinite number of points in Hilbert space, meaning that the dimension K of the classical memory required for the tracking is… 

Figures and Tables from this paper

Nonlinear algebra in 3 D computer vision

I study computational algebraic geometry—an amusing, somewhat more broad name for this field is nonlinear algebra. This field is firmly anchored to its algorithmic techniques—traditionally, symbolic

References

SHOWING 1-10 OF 54 REFERENCES

Tracking an open quantum system using a finite state machine: Stability analysis

A finite-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps,

How many bits does it take to track an open quantum system?

It is shown that, for any ergodic master equation, one can expect to find an adaptive monitoring scheme on the bath that can confine the system state to jumping between only K states, for some K ≥ (D - 1)(2) + 1.

Symmetries and physically realisable ensembles for open quantum systems

S symmetry-based techniques that potentially greatly reduce the difficulty of finding a subset of all possible PREs are developed and an analysis of previously known PREs using the developed techniques provides new insights and lays the foundation for future studies of higher dimensional systems.

Stochastic feedback control of quantum transport to realize a dynamical ensemble of two nonorthogonal pure states

A Markovian open quantum system which relaxes to a unique steady state ${\ensuremath{\rho}}_{\mathrm{ss}}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure

Inequivalence of pure state ensembles for open quantum systems: the preferred ensembles are those that are physically realizable.

This work presents the necessary and sufficient conditions for a given ensemble to be PR, and illustrates the method by showing that the coherent state ensemble is not PR for an atom laser.

Stochastic differential equations anda posteriori states in quantum mechanics

In recent years a consistent theory describing measurements continuous in time in quantum mechanics has been developed. The result of such a measurement is a“trajectory”for one or more quantities

Quantum Processes Systems, and Information

A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three

The quantum-state diffusion model applied to open systems

A model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation, derived from a density

Probability relations between separated systems

  • E. Schrödinger
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1936
The paper first scrutinizes thoroughly the variety of compositions which lead to the same quantum-mechanical mixture (as opposed to state or pure state). With respect to a given mixture every state

Quantum Measurement and Control

The control of individual quantum systems promises a new technology for the 21st century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and
...