Informational power of quantum measurements

  title={Informational power of quantum measurements},
  author={Michele Dall’Arno and Giacomo Mauro D’Ariano and Massimiliano F. Sacchi},
  journal={Physical Review A},
We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational power corresponds to the classical capacity of a quantum-classical channel. We restate the problem of evaluating the informational power as the maximization of the accessible information of a suitable ensemble. We provide a numerical algorithm to find an optimal… 

Figures from this paper

The application of optimal quantum measurements to quantum channels

It is found that traditional optimal measurement techniques do not necessarily maximise information transfer rates and therefore the maximisation of the mutual information must be done explicitly.

The information capacity of entanglement-assisted continuous variable quantum measurement

The present paper is devoted to the investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These

Device-Independent Tests of Quantum Measurements.

The main result is to provide a closed-form, full characterization of the set of input-output correlations that can be generated by an arbitrarily given quantum measurement, and to discuss its geometrical interpretation.

On the Proof of the Entanglement-assisted Coding Theorem for a Quantum Measurement Channel

The notion of conditional entropy in hybrid (quantum-classical) systems and some of its properties are considered and the proof of the coding theorem for the entanglement-assisted classical capacity of the measurement channel with arbitrary output alphabet is refined.

Efficient Accessible Bounds to the Classical Capacity of Quantum Channels.

A method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements, reconstruction of sets of conditional probabilities, and classical optimization is presented.

The information capacity of entanglement-assisted continuous variable measurement

The present paper is devoted to investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities

Information capacity of a quantum observable

The classical capacities of quantum-classical channels corresponding to measurement of observables, and formulas for unassisted and entanglement-assisted classical capacities C and Cea, to show that Cea for the measurement channel is related to the χ-quantity for the dual ensemble in the same way as C isrelated to the accessible information.

Coherence of Quantum Ensemble as a Dual to Uncertainty for a Single Observable

  • D. Kronberg
  • Physics
    Lobachevskii Journal of Mathematics
  • 2019
The coherence of an ensemble of quantum states is considered — a quantity having a similarity with the uncertainty of the quantum observable that arises from the entropic uncertainty relations. We

Optimal signal states for quantum detectors

The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities and provides analytical proofs of optimality in some relevant cases.

Tradeoff Relations Between Accessible Information, Informational Power, and Purity

The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa–Robb–Wootters lower bound to the accessible information.



Iterative procedure for computing accessible information in quantum communication

An iterative algorithm is presented that finds the optimal measurement for extracting the accessible information in any quantum communication scenario by a steepest-ascent approach toward the extremal point, following the gradient uphill in sufficiently small steps.

A ‘Pretty Good’ Measurement for Distinguishing Quantum States

A simple general prescription for a measurement that is typically not optimal but appears to be quite good is considered, which seems to be particularly good when the states to be distinguished are equally likely and almost orthogonal.

Additivity of the classical capacity of entanglement-breaking quantum channels

We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the

Purification of noisy quantum measurements

We consider the problem of improving noisy quantum measurements by suitable preprocessing strategies making many noisy detectors equivalent to a single ideal detector. For observables pertaining to

Information and quantum measurement

Given a finite number of quantum states with {\em a priori} probabilities, the positive operator-valued measure that maximizes the Shannon mutual information is investigated. The group covariant case

Coding Theorems for Quantum Channels

An emphasis is made on recent results, such as general quantum coding theorems including cases of infinite (possibly continuous) alphabets and constrained inputs, reliability function for pure state channels and quantum Gaussian channel.

Channel correction via quantum erasure.

  • F. Buscemi
  • Physics, Computer Science
    Physical review letters
  • 2007
The present analysis also applies to channels for which perfect quantum erasure is impossible, thus extending the original quantum eraser arrangement, and naturally embodies a general information-disturbance trade-off.

Towards a Unified Approach to Information-Disturbance Tradeoffs in Quantum Measurements

We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys. Rev. Lett. 100, 210504 (2008)] makes it possible to

Distilling common randomness from bipartite quantum states

A single-letter formula for the optimal tradeoff between the extracted common randomness and classical communication rate is obtained for the special case of classical-quantum correlations.