# Free randomness can be amplified

@article{Colbeck2012FreeRC, title={Free randomness can be amplified}, author={Roger Colbeck and Renato Renner}, journal={Nature Physics}, year={2012}, volume={8}, pages={450-454} }

Bell’s equations enable scientists to test the fundamental implications of quantum physics. A central tenet of this idea is that the choice of measurement is truly random. Researchers now show that some Bell experiments can even increase randomness in cases where choice is not entirely free. The concept could increase the usefulness of weakly random sources for more thorough tests of quantum mechanics.

## Figures from this paper

## 235 Citations

Certified randomness in quantum physics

- Computer Science, PhysicsNature
- 2016

Encryption technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities, which are referred to as device-independent because they do not rely on any modelling of the devices.

Randomness and Non-Locality

- Mathematics
- 2016

The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude…

Effects of reduced measurement independence on Bell-based randomness expansion.

- Physics, MedicinePhysical review letters
- 2012

A no-signaling model with reduced "free will" is considered and the adversary’s capabilities in the task of randomness expansion are bound.

On the Sufficiency of the Wavefunction

- Physics
- 2015

Within quantum theory, the Born rule restricts our ability to predict measurement outcomes. However, could it be that this restriction is not fundamental, but instead due to the quantum wavefunction…

Quantum random number generators

- Physics
- 2017

In mathematics and computer science, random numbers have the role of a resource for assisting proofs, making cryptography secure, and enabling computational protocols. This role motivates efforts to…

High speed device-independent quantum random number generation without detection loophole

- Physics, Medicine2018 Conference on Lasers and Electro-Optics (CLEO)
- 2018

An experimental study of device-independent quantum random number generation based on an detection-loophole free Bell test with entangled photons, which achieves a final random bit rate of 114 bits/s.

Limited measurement dependence in multiple runs of a Bell test

- Physics
- 2013

The assumption of free will - the ability of an experimentalist to make random choices - is central to proving the indeterminism of quantum resources, the primary tool in quantum cryptography.…

Uncertainty principle guarantees genuine source of intrinsic randomness

- Mathematics, PhysicsQuantum Inf. Process.
- 2014

This article shows that the minimum amount of intrinsic randomness that can be guaranteed for arbitrarily prepared state of the system is quantified by the amount of (un)certainty.

Kolmogorov amplification from Bell correlation

- Computer Science2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

It is established that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource.

Device Independent Random Number Generation

- Physics, Mathematics
- 2014

Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true…

## References

SHOWING 1-10 OF 37 REFERENCES

Free will and quantum mechanics

- Physics
- 2011

A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper…

Hidden variable models for quantum theory cannot have any local part.

- Physics, MedicinePhysical review letters
- 2008

This Letter shows the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a nontrivial local part, such as the model proposed by Leggett.

No extension of quantum theory can have improved predictive power

- Physics, MedicineNature communications
- 2011

This work says that no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself, under the assumption that measurements can be chosen freely.

Experimenter's freedom in Bell's theorem and quantum cryptography (7 pages)

- Physics
- 2006

Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings.…

Wringing out better Bell inequalities

- Mathematics
- 1989

Abstract Local realism implies constraints on the statistics of two physically separated systems. These constraints, known collectively as Bell inequalities, can be violated by quantum mechanics. We…

Going Beyond Bell’s Theorem

- Mathematics, Physics
- 1989

Bell’s Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could…

Quantum nonlocality as an axiom

- Mathematics
- 1994

In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a…

Random numbers certified by Bell’s theorem

- Physics, Computer ScienceNature
- 2010

It is shown that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness, and it is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device.

Violation of local realism with freedom of choice

- Economics, MathematicsProceedings of the National Academy of Sciences
- 2010

This paper presents an experiment that violates Bell’s inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions.

The Free Will Theorem

- Mathematics, Physics
- 2006

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is…