Recently, the principle of information causality has appeared as a good candidate for an information-theoretic principle that would single out quantum correlations among more general non-signalling models. Here we present results going in this direction; namely we show that part of the boundary of quantum correlations actually emerges from information causality. I.
We introduce a fundamental concept -closed sets of correlations -for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum non-locality is limited, and for finding constraints on physical theories beyond quantum mechanics.Correlations are a central concept in physics. While in classical physics correlations must satisfy two fundamental principles -causality and locality -in quantum mechanics (QM) the latter must be abandoned. This remarkable feature, known as quantum non-locality, is at the heart of quantum information processing and allows tasks to be performed which would be impossible classically, such as secure cryptography [1] and the reduction of communication complexity [2].However, non-local correlations stronger than those allowed by QM can also respect relativistic causality [3]. These non-signaling post-quantum correlations have been subject to intensive research [4,5,6,7,8,9,10,11], and were shown to have strong information-theoretic consequences, allowing for powerful tasks -impossible in QM -to be peformed. For instance, certain post-quantum correlations collapse communication complexity [7,10]; allow for better-than-classical 'non-local computation ' [8]; and violate 'information causality' [11].Here we introduce a fundamental concept -closed sets of correlations -underlying the structure of non-local correlations. We argue that physically significant sets of correlations must be closed under a natural class of operations.The immediate relevance of this concept if two-fold. First, we note that all information-theoretic principles correspond to closed sets of correlations. For instance, the set of correlations that do not make communication complexity trivial is closed. If two different information-theoretic principles turn out to correspond to the same closed set then they are in fact equivalent as far as the resources needed to implement them are concerned. Therefore, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This also leads one to ask: is there an infinite number of closed sets or only finitely many? If it was found that only a small number of closed sets can exist, then most informationtheoretic principles would turn out to be the same.Even more importantly, correlations allowed by any selfconsistent physical theory must form a closed set. For instance in classical mechanics, it is impossible to generate non-local correlations from local ones. Similarly, post-quantum correlations cannot be generated within the framework of QM. From this perspective, the concept of closure gives ...
We study the effects of localization on quantum state transfer in spin chains. We show how to use quantum error correction and multiple parallel spin chains to send a qubit with high fidelity over arbitrary distances, in particular, distances much greater than the localization length of the chain.
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine learning today. We present quantum algorithms for training and evaluating feedforward neural networks based on the canonical classical feedforward and backpropagation algorithms. Our algorithms rely on an efficient quantum subroutine for approximating inner products between vectors in a robust way, and on implicitly storing intermediate values in quantum random access memory for fast retrieval at later stages. The running times of our algorithms can be quadratically faster in the size of the network than their standard classical counterparts since they depend linearly on the number of neurons in the network, and not on the number of connections between neurons. Furthermore, networks trained by our quantum algorithm may have an intrinsic resilience to overfitting, as the algorithm naturally mimics the effects of classical techniques used to regularize networks. Our algorithms can also be used as the basis for new quantum-inspired classical algorithms with the same dependence on the network dimensions as their quantum counterparts but with quadratic overhead in other parameters that makes them relatively impractical.
We propose simple protocols for performing quantum noise spectroscopy based on the method of transfer tensor maps (TTM), [Phys. Rev. Lett. 112, 110401 (2014)]. The TTM approach is a systematic way to deduce the memory kernel of a time-nonlocal quantum master equation via quantum process tomography. With access to the memory kernel it is possible to (1) assess the non-Markovianity of a quantum process, (2) reconstruct the noise spectral density beyond pure dephasing models, and (3) investigate collective decoherence in multiqubit devices. We illustrate the usefulness of TTM spectroscopy on the IBM Quantum Experience platform, and demonstrate that the qubits in the IBM device are subject to mild non-Markovian dissipation with spatial correlations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.