Maximum Quantum Non-Locality is not always Sufficient for Device-Independent Randomness Generation
- URL: http://arxiv.org/abs/2408.03665v1
- Date: Wed, 7 Aug 2024 10:07:39 GMT
- Title: Maximum Quantum Non-Locality is not always Sufficient for Device-Independent Randomness Generation
- Authors: Ravishankar Ramanathan, Yuan Liu, Stefano Pironio,
- Abstract summary: We present families of $n$-player non-local games for $n geq 2$ and families of non-local behaviors on the quantum boundary that do not allow to certify any randomness against a classical adversary.
Our results show the existence of a form of bound randomness against classical adversaries, highlighting that device-independent randomness and quantum non-locality can be maximally inequivalent resources.
- Score: 3.7482527016282963
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The outcomes of local measurements on entangled quantum systems can be certified to be genuinely random through the violation of a Bell Inequality. The randomness of the outcomes with respect to an adversary is quantified by the guessing probability, conditioned upon the observation of a specific amount of Bell violation or upon the observation of the entire input-output behavior. It has been an open question whether standard device-independent randomness generation protocols against classical or quantum adversaries can be constructed on the basis of any arbitrary Bell inequality, i.e., does there exist a Bell inequality for which the guessing probability is one for any chosen input even upon observing the maximal violation of the inequality? A strengthened version of the question asks whether there exists a quantum behavior that exhibits maximum non-locality but zero certifiable randomness for any arbitrary input. In this paper, we present an affirmative answer to both questions by constructing families of $n$-player non-local games for $n \geq 2$ and families of non-local behaviors on the quantum boundary that do not allow to certify any randomness against a classical adversary. Our results show the existence of a form of bound randomness against classical adversaries, highlighting that device-independent randomness and quantum non-locality can be maximally inequivalent resources.
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