scholarly journals Bound on genuine multipartite correlations from the principle of information causality

2011 ◽  
Vol 11 (11&12) ◽  
pp. 948-956
Author(s):  
Yang Xiang ◽  
Wei Ren
Keyword(s):  
Quantum Theory ◽  
Broad Class ◽  
Quantum Correlations ◽  
Physical Principle ◽  
Information Theoretic ◽  
Particle Correlations ◽  
Theoretic Proof ◽  
Information Causality ◽  
No Signaling ◽  
Maximal Violation

Quantum mechanics is not the unique no-signaling theory which is endowed with stronger-than-classical correlations, and there exists a broad class of no-signaling theories allowing even stronger-than-quantum correlations. The principle of information causality has been suggested to distinguish quantum theory from these nonphysical theories, together with an elegant information-theoretic proof of the quantum bound of two-particle correlations. In this work, we extend this to genuine $N$-particle correlations that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. We first express Svetlichny's inequality in terms of multipartite no-signaling boxes, then prove that the strongest genuine multipartite correlations lead to the maximal violation of information causality. The maximal genuine multipartite correlations under the constraint of information causality is found to be equal to the quantum mechanical bound. This result consolidates information causality as a physical principle defining the possible correlations allowed by nature, and provides intriguing insights into the limits of genuine multipartite correlations in quantum theory.

scholarly journals Information-Theoretic Generalization Bounds for Meta-Learning and Applications

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 126
Author(s):  
Sharu Theresa Jose ◽  
Osvaldo Simeone
Keyword(s):  
Learning Algorithm ◽  
Broad Class ◽  
Performance Measure ◽  
Training Data ◽  
Learning To Learn ◽  
Data Set ◽  
Information Theoretic ◽  
Meta Learning ◽  
Task Training ◽  
Test Sets

Meta-learning, or “learning to learn”, refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key performance measure for meta-learning is the meta-generalization gap, that is, the difference between the average loss measured on the meta-training data and on a new, randomly selected task. This paper presents novel information-theoretic upper bounds on the meta-generalization gap. Two broad classes of meta-learning algorithms are considered that use either separate within-task training and test sets, like model agnostic meta-learning (MAML), or joint within-task training and test sets, like reptile. Extending the existing work for conventional learning, an upper bound on the meta-generalization gap is derived for the former class that depends on the mutual information (MI) between the output of the meta-learning algorithm and its input meta-training data. For the latter, the derived bound includes an additional MI between the output of the per-task learning procedure and corresponding data set to capture within-task uncertainty. Tighter bounds are then developed for the two classes via novel individual task MI (ITMI) bounds. Applications of the derived bounds are finally discussed, including a broad class of noisy iterative algorithms for meta-learning.

scholarly journals Quantum Mechanics and Global Determinism

Quanta ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Emily Christine Adlam
Keyword(s):  
Quantum Mechanics ◽  
Quantum Correlations ◽  
Deterministic Theory ◽  
No Signaling ◽  
Open Question ◽  
Global Determinism

It is proposed that certain features of quantum mechanics may be perspectival effects, which arise because experiments performed on locally accessible variables can only uncover a certain subset of the correlations exhibited by an underlying deterministic theory. This hypothesis is used to derive the no-signaling principle, thus resolving an open question regarding the apparently fine-tuned nature of quantum correlations. Some potential objections to this approach are then discussed and answered.Quanta 2018; 7: 40–53.

scholarly journals Reality, Indeterminacy, Probability, and Information in Quantum Theory

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 747
Author(s):  
Arkady Plotnitsky
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum Phenomena

Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.

scholarly journals Relativistic independence bounds nonlocality

2019 ◽  
Vol 5 (4) ◽  
pp. eaav8370 ◽  
Author(s):  
Avishy Carmi ◽  
Eliahu Cohen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Correlations ◽  
Physical Principle ◽  
Quantum Nonlocality ◽  
Measuring Instruments ◽  
Uncertainty Relations ◽  
The Past ◽  
Nonlocal Correlations

If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here, it is shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters’ choices of measuring instruments. We prove that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers.

Quantum theory, the Church–Turing principle and the universal quantum computer

1985 ◽  
Vol 400 (1818) ◽  
pp. 97-117 ◽  
Keyword(s):  
Quantum Theory ◽  
Complexity Theory ◽  
Turing Machine ◽  
Physical System ◽  
Quantum Computer ◽  
Physical Principle ◽  
Universal Turing Machine ◽  
Universal Quantum ◽  
Computing Machines ◽  
The Church

It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it. The intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than Everett’s. Some of the numerous connections between the quantum theory of computation and the rest of physics are explored. Quantum complexity theory allows a physically more reasonable definition of the ‘complexity’ or ‘knowledge’ in a physical system than does classical complexity theory.

Quantum theory from quantum information: the purification route

2013 ◽  
Vol 91 (6) ◽  
pp. 475-478 ◽  
Author(s):  
Giulio Chiribella ◽  
Xiao Yuan
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Theory ◽  
Quantum Information ◽  
Foundations Of Quantum Mechanics ◽  
Mathematical Structure ◽  
Mathematical Language ◽  
Standard Quantum ◽  
Information Theoretic

Quantum information provided a new angle on the foundations of quantum mechanics, where the emphasis is placed on operational tasks pertaining to information-processing and computation. In this spirit, several authors have proposed that the mathematical structure of quantum theory could (and should) be rebuilt from purely information-theoretic principles. Here we review the particular route proposed by D'Ariano, Perinotti, and one of the authors (Chiribella et al. Phys. Rev. A, 84, 012311 (2011)), with the purpose of giving a synopsis of the informational principles therein, along with a translation of those principles into the mathematical language of standard quantum theory.

scholarly journals ELEMENTS OF INFORMATION-THEORETIC DERIVATION OF THE FORMALISM OF QUANTUM THEORY

2003 ◽  
Vol 01 (03) ◽  
pp. 289-300 ◽  
Author(s):  
ALEXEI GRINBAUM
Keyword(s):  
Quantum Theory ◽  
Conceptual Framework ◽  
Information Theoretic ◽  
Quantum Formalism

Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several approaches, one can retrieve more of the conventional quantum formalism.

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