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Device-independent dimension test in a multiparty Bell experiment

Zhaohui Wei, Jamie Sikora
2019 New Journal of Physics  
A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions  ...  In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment.  ...  NRF-NRFF2013-13, the National Key R&D Program of China, Grant No. 2018YFA0306703, and the start-up funds of Tsinghua University, Grant No. 53330100118.  ... 
doi:10.1088/1367-2630/ab1514 fatcat:qrcfrfwu5bgj5dscthen6blutm

Device-independent dimension test in a multiparty Bell experiment [article]

Zhaohui Wei, Jamie Sikora
2019 arXiv   pre-print
A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions  ...  In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment.  ...  Since each correlation is generated using d-dimensional local Hilbert spaces, d is a natural upper bound on the smallest Hilbert space dimension.  ... 
arXiv:1707.03125v2 fatcat:xfmyvh5epnekzpyud5e76j4t3u

Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation

Jamie Sikora, Antonios Varvitsiotis, Zhaohui Wei
2016 Physical Review Letters  
In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation.  ...  A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation.  ...  Research at the Centre for Quantum Technologies at the National University of Singapore is partially funded by the Singapore Ministry of Education and the National Research Foundation, also through the  ... 
doi:10.1103/physrevlett.117.060401 pmid:27541446 fatcat:ucknnodbeveyvoiv47otaxdxba

Greenberger-Horne-Zeilinger test for multi-dimension and arbitrary time nodes entangled histories

Junkai Dong, Yi-Ming Chen, Da Xu, Zhang-Qi Yin
2017 Science Bulletin  
Only when both the number of time nodes and system dimensions approach to infinity, the minimum of the witness for classical and quantum entangled histories are identical.  ...  Then, we define a witness to distinguish between the quantum entangled histories and the classical histories.  ...  Acknowledgments We would like to thank Tongcang Li for valuable suggestions and insights. We would also like to thank Dr. Ryu for his special insights for the discussion of odd dimension.  ... 
doi:10.1016/j.scib.2017.08.010 fatcat:lpvay3cyn5fe3fsfx77hpkqgmu

Identifying nonconvexity in the sets of limited-dimension quantum correlations

John Matthew Donohue, Elie Wolfe
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if  ...  Here we find that the set of distributions compatible with sharing quantum states subject to some sufficiently restricted dimension is neither convex nor a superset of the classical distributions.  ...  ACKNOWLEDGMENTS We are grateful to Joshua Combes, Tobias Fritz, Ravi  ... 
doi:10.1103/physreva.92.062120 fatcat:22dmdbkp5rf6xg2qlrygrwuuu4

Quantum state space dimension as a quantum resource

A. Plastino, G. Bellomo, A. R. Plastino
2015 International Journal of Quantum Information  
We argue that the dimensionality of the space of quantum systems' states should be considered as a legitimate resource for quantum information tasks.  ...  The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically correlated states in spaces of dimension large enough.  ...  Here, we propose to consider the dimension of the Hilbert space as a legitimate resource for quantum information processing.  ... 
doi:10.1142/s0219749915500392 fatcat:7nf6h4f65vhkrkopwwlqpzzmim

Quantum Gravity, Information Theory and the CMB

Achim Kempf
2018 Foundations of physics  
We also discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields suffices to determine the spacetime metric.  ...  In particular, we discuss the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlators of the fluctuations of quantum fields.  ...  Hilbert space of functions on the manifold.  ... 
doi:10.1007/s10701-018-0163-2 fatcat:akiqt2yfybfi5hyhwvp46zoyma

Hypersensitivity to Perturbation: An Information-Theoretical Characterization of Classical and Quantum Chaos [chapter]

Rüdiger Schack, Carlton M. Caves
1997 Quantum Communication, Computing, and Measurement  
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing  ...  In this paper we give a brief overview of our work on hypersensitivity to perturbation in classical and quantum systems. *  ...  The 2 10 quartets seem to be rather uniformly distributed in a n d = 46-dimensional Hilbert space (see [8] for a definition of the number of explored Hilbert-space dimensions, n d ).  ... 
doi:10.1007/978-1-4615-5923-8_34 fatcat:ueuul3kdfba6jmvi6akgt3wdru

Operational characterization of quantumness of unsteerable bipartite states

Debarshi Das, Bihalan Bhattacharya, Chandan Datta, Arup Roy, C. Jebaratnam, A. S. Majumdar, R. Srikanth
2018 Physical Review A  
Generalizing the concept of superlocality, we define as super-correlation, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states  ...  This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.  ...  BB, CJ and ASM acknowledge the financial support from project SR/S2/LOP-08/2013 of the Department of Science and Technology (DST), government of India.  ... 
doi:10.1103/physreva.97.062335 fatcat:owjr5zx4ofewbe5gcbhjswpzw4

Quantifying quantum computational complexity via information scrambling [article]

Arash Ahmadi, Eliska Greplova
2022 arXiv   pre-print
This connection allows us to establish a novel, experimentally scalable way to approximate magic monotones in an arbitrary Hilbert space dimension and therefore evaluate the amount of quantum resources  ...  In this work, we provide a new perspective on calculating magic monotones by connecting them to the concept of information scrambling.  ...  The definition of T-gate for 2-dimensional Hilbert space is T 2 = 1 0 0 e iπ/4 (B5) The generalization of T-gate to higher dimensional Hilbert spaces is not so straightforward [34] .  ... 
arXiv:2204.11236v2 fatcat:d4sacghxsfbilgtwiaf6z4jmti

Bounding the dimension of bipartite quantum systems

Tamás Vértesi, Károly F. Pál
2009 Physical Review A. Atomic, Molecular, and Optical Physics  
Let us consider the set of joint quantum correlations arising from two-outcome local measurements on a bipartite quantum system.  ...  We prove that no finite dimension is sufficient to generate all these sets.  ...  Acknowledgments T.V. has been supported by a János Bolyai Grant of the Hungarian Academy of Sciences.  ... 
doi:10.1103/physreva.79.042106 fatcat:aggejd6nijeu5b5ig5ecq66lqi

Quantum Gravity In De Sitter Space [article]

Edward Witten
2001 arXiv   pre-print
We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension.  ...  We give a definition of the quantum Hilbert space using the asymptotic behavior in the past and future, without requiring detailed microscopic knowledge.  ...  ), as one desires to make the Hilbert space H finite-dimensional.  ... 
arXiv:hep-th/0106109v1 fatcat:ysgtbwufqzg4ln6xi2lp5srcoi

Quantum Compression of Tensor Network States [article]

Ge Bai, Yuxiang Yang, Giulio Chiribella
2019 arXiv   pre-print
We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family.  ...  The bound is determined by the minimum cut of a suitable flow network, and is related to the flow of information from the manifold of parameters that specify the states to the physical systems in which  ...  The algorithm Here we outline a general quantum algorithm for compressing families of pure states lying in a low-dimensional subspace of a high-dimensional quantum system.  ... 
arXiv:1904.06772v2 fatcat:ansjsv3pjbgs3petgzdc6nplii

Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement

Yaoyun Shi, Yufan Zhu
2008 SIAM journal on computing (Print)  
We initiate the study of quantifying nonlocalness of a bipartite measurement by the minimum amount of classical communication required to simulate the measurement.  ...  same set of functions; (b) A local hidden variable model needs only a constant amount of communication to create, within an arbitrarily small statistical distance, a distribution resulted from local measurements  ...  Acknowledgments We are indebted to Wei Huang, Amnon Ta-Shma, and the anonymous reviewers for their valuable suggestions on improving the presentation of this paper.  ... 
doi:10.1137/050644768 fatcat:kpwnqvedtvei3cx4co2x6zxaqy

Generation and confirmation of a (100 x 100)-dimensional entangled quantum system

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, A. Zeilinger
2014 Proceedings of the National Academy of Sciences of the United States of America  
Here we present the creation of a (100x100)-dimensional entangled quantum system, using spatial modes of photons.  ...  For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations.  ...  Moreover, the entangled dimensions of the whole Hilbert space also play a very interesting role in quantum computation: high-dimensional systems can be used to simplify the implementation of quantum logic  ... 
doi:10.1073/pnas.1402365111 pmid:24706902 pmcid:PMC4035950 fatcat:gezptcugvvgmvhitz46vlu6nua
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