Correlation and Randomness

• Research unit: COST
• Project number: C12.0113

Key words (English)

Quantum communication complexity; quantum channels; nonlocality; convex optimization; quantum foundation

Research programs (English)

COST-Action MP1006 - Fundamental Problems in Quantum Physics

Short description (English)

Randomness is a central resource in information processing, e.g., cryptography. It is known that without further assumptions, it is generally impossible to generate strong randomness from weak. Motivated by optimistic preliminary results by other authors, we propose to investigate whether (and which) physical assumptions -- such as the non-signaling postulate of relativity -- allow for amplifying arbitrarily weak randomness to close-to-perfect. The key towards such a statement are results showing the impossibility to base quantum-physical behavior on pre-existing classical information -- as long as the measurements are assumed to be chosen at least partially freely. The most important such results have been derived by Kochen/Specker and Bell. We believe that a systematic study in particular of non-local correlations allows for obtaining insight into the possibilities and limitations of randomness amplification. A second goal of the proposed study is a simple yet tight characterization of quantum as opposed to super-quantum correlations. Such a criterion is intensively sought for, yet still outstanding.

Further information (English)

Full name of research-institution/enterprise: Università della Svizzera italiana USI Faculty of Informatics

Partners and International Organizations (English)

AT; BE; CZ; FI; FR; DE; EL; HU; IE; IL; IT; LT; MT; PL; PT; RS; SK; SI; ES; CH; UK

Abstract (English)

The project consists of two lines of research in quantum communication complexity, which are strictly related. The first line concerns the computation of the minimal amount of classical communication required for simulating quantum channels. The motivation for studying this problem is twofold. The first motivation is practical, as the minimal amount of classical communication required for simulating a quantum channel, called the communication complexity of the channel, provides the ultimate power of quantum communication in terms of classical resources. Indeed, in a communication complexity scenario, a quantum channel cannot replace an amount of classical communication greater than its communication complexity. The second motivation is related to a quantum foundational question concerning the nature of the quantum state. Indeed, if the communication complexity of a noiseless quantum channel grows more than n 2^n, 'n' being the quantum channel capacity, then it is possible to show that the quantum state is part of the classical definition of state in any classical simulation of quantum systems, in the limit of infinite qubits. Thus, the proof that the communication grows more n 2^n implies the same conclusion of the Pusey-Barrett-Rudolph theorem without any preparation independence hypothesis. The second line of research concerns the computation of the minimal amount of classical communication required for simulating nonlocal correlations. This quantity, which we called 'nonlocal capacity', provides a measure of nonlocality in terms of classical communication, as an alternative to the strength of Bell inequality violation. After introducing a method that reduces the computation of the nonlocal capacity to a convex optimization problem, we have studied an approach for finding the optimal set of measurements that maximize the measure of nonlocality for given entangled states. This line of research is part of a currently active collaboration with the experimental group of Andre Stefanov in Bern. The introduced approach allows us to efficiently find the best experimental configuration providing the strongest evidence of nonlocal correlations.

References in databases (English)

Swiss Database: COST-DB of the State Secretariat for Education and Research Hallwylstrasse 4 CH-3003 Berne, Switzerland Tel. [phone] Swiss Project-Number: C12.0113