# Entropic uncertainty and measurement reversibility

@article{Berta2015EntropicUA, title={Entropic uncertainty and measurement reversibility}, author={Mario Berta and Stephanie Wehner and Mark M. Wilde}, journal={arXiv: Quantum Physics}, year={2015} }

The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the "uncertainty witness" lower bound in the EUR-QSI is not a function of…

## 70 Citations

Entropic uncertainty relations in the spin-1 Heisenberg model

- PhysicsQuantum Inf. Process.
- 2019

The dynamical evolution of QMA-EUR is derived for various incompatible measurements on Pauli operators and SU(3) generators in the Heisenberg XXX and XYZ models and it is declared that the dynamics of the entropic uncertainty of interest are approximately anti-correlated with that of negativity.

Entropic uncertainty relations for quantum information scrambling

- PhysicsCommunications Physics
- 2019

Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an…

Tighter Bound of Entropic Uncertainty under the Unruh Effect

- PhysicsAnnalen der Physik
- 2020

The uncertainty principle limits the ability to simultaneously predict measurement outcomes for two non‐commuting observables of a quantum particle. However, the uncertainty can be violated by…

Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

- PhysicsQuantum Inf. Process.
- 2018

The aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs and claims that the entropics uncertainty relation could be a promising tool with which to probe entanglement in current architecture.

Exploration of entropic uncertainty relation for two accelerating atoms immersed in a bath of electromagnetic field

- PhysicsQuantum Inf. Process.
- 2019

This paper studies the dynamics of quantum-memory-assisted entropic uncertainty relation for two accelerating atoms coupled with a bath of fluctuating electromagnetic field and finds that the mixedness is bound up with the entropics uncertainty.

Characterizing the dynamics of entropic uncertainty for multi-measurement

- Physics
- 2020

Uncertainty principle lies at the heart of quantum theory and is regarded as a vital property essentially differing from the rule in classical physics. We herein study the dynamics of the entropic…

Steering the measured uncertainty under decoherence through local ${\mathcal{P}\mathcal{T}}$ -symmetric operations

- Physics
- 2018

The uncertainty principle is viewed as one of the appealing properties in the context of quantum mechanics, which intrinsically offers a lower bound with regard to the measurement outcomes of a pair…

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

- Computer Science
- 2016

This paper applies and extends results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics.

Unveiling the decoherence effect of noise on the entropic uncertainty relation and its control by partially collapsed operations

- Physics
- 2018

In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence.…

Entropic methodology for entanglement measures

- Physics, Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2018

## References

SHOWING 1-10 OF 59 REFERENCES

Position-momentum uncertainty relations in the presence of quantum memory

- Physics
- 2014

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements.…

Entropic uncertainty relations and their applications

- Physics, Computer Science
- 2017

This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements.

Uncertainty relation for smooth entropies.

- Computer SciencePhysical review letters
- 2011

This paper shows that security of quantum key distribution protocols implies security of smooth entropies, and shows that this security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model.

Relative entropy derivation of the uncertainty principle with quantum side information

- Physics
- 2011

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof…

Uncertainty, monogamy, and locking of quantum correlations

- PhysicsIEEE Transactions on Information Theory
- 2005

The results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost.

Recoverability in quantum information theory

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

If the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other.

Uncertainty relations from simple entropic properties.

- Computer SciencePhysical review letters
- 2012

This work shows that a single technique applies to several entropic quantities, including the von Neumann entropy, min- and max-entropies, and the Rényi entropies.

Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities

- Mathematics
- 2013

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy…

Conjectured strong complementary information tradeoff.

- Computer SciencePhysical review letters
- 2009

A special case for certain conjugate observables is proved by adapting a similar result found by Christandl and Winter pertaining to quantum channels, and possible applications to the decoupling of quantum systems and for security analysis in quantum cryptography are discussed.

Entanglement Sampling and Applications

- Computer ScienceIEEE Transactions on Information Theory
- 2015

This work establishes the first entropic uncertainty relations with quantum side information that are nontrivial whenever E is not maximally entangled with A, and is able to prove optimality of quantum cryptographic schemes in the noisy-storage model.