Universality and Optimality in the Information–Disturbance Tradeoff

@article{Hashagen2018UniversalityAO,
  title={Universality and Optimality in the Information–Disturbance Tradeoff},
  author={Anna-Lena Hashagen and M. Wolf},
  journal={Annales Henri Poincar{\'e}},
  year={2018},
  volume={20},
  pages={219-258}
}
We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann measurement, then the optimal tradeoff can always be achieved within a two-parameter family of quantum devices that is independent of the chosen distance measures. This form of almost universal optimality holds under mild assumptions on the distance measures such as… Expand

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References

SHOWING 1-10 OF 42 REFERENCES
Error-tradeoff and error-disturbance relations for incompatible quantum measurements
  • C. Branciard
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences
  • 2013
TLDR
This paper quantifies precisely Heisenberg’s intuition on the disturbance of an observable induced by the approximate measurement of another one and derives a stronger error-disturbance relation for this scenario. Expand
Measurement Uncertainty for Finite Quantum Observables
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to computeExpand
Uncertainty relations: An operational approach to the error-disturbance tradeoff
TLDR
This work defines error and disturbance in an operational manner in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever, and derives new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observable systems. Expand
Measurement-Disturbance Tradeoff Outperforming Optimal Cloning
One of the characteristic features of quantum mechanics is that every measurement that extracts information about a general quantum system necessarily causes an unavoidable disturbance to the stateExpand
Quantum f-divergences and error correction
TLDR
It is shown that the quantum f-divergences are monotonic under the dual of Schwarz maps whenever the defining function is operator convex, and an integral representation for operator conveX functions on the positive half-line is provided, which is the main ingredient in extending previously known results on the monotonicity inequality and the case of equality. Expand
Trade-off relation between information and disturbance in quantum measurement
When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed toExpand
Colloquium: Quantum root-mean-square error and measurement uncertainty relations
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurementExpand
The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation
TLDR
A continuity theorem for Stinespring's dilation is proved: if two quantum channels are close in cb-norm, then it is always possible to find unitary implementations which areClose in operator norm, with dimension-independent bounds. Expand
Proof of Heisenberg's error-disturbance relation.
TLDR
It is shown that despite recent claims to the contrary, Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum. Expand
Noise and disturbance in quantum measurements: an information-theoretic approach.
We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have toExpand
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