Multi-Receiver Dense Coding in High-Dimensional Hilbert Spaces

2014 ◽  
Author(s):  
Sara Bagheri ◽  
Saied Hosseini Khayyat ◽  
Mehdi Saberi
Keyword(s):  
Hilbert Spaces ◽  
High Dimensional ◽  
Dense Coding

scholarly journals High-dimensional temporal mode propagation in a turbulent environment

2021 ◽  
Vol 21 (3&4) ◽  
pp. 233-254
Author(s):  
Quanzhen Ding ◽  
Rupak Chatterjee ◽  
Yuping Huang ◽  
Ting Yu
Keyword(s):  
Hilbert Spaces ◽  
Quantum Key Distribution ◽  
Communication Channel ◽  
Weather Conditions ◽  
High Dimensional ◽  
Turbulent Environment ◽  
Temporal Mode ◽  
Temporal Modes ◽  
Maritime Environment ◽  
New Framework

Temporal modes of photonic quantum states, intrinsically possess high dimensional Hilbert spaces, provide a new framework to develop a robust free-space quantum key distribution (QKD) scheme in a maritime environment. We show that the high-dimensional temporal modes can be used to fulfill a persistent communication channel to achieve high photon-efficiency even in severe weather conditions. We identify the parameter regimes that allow for a high-fidelity quantum information transmission. We also examine how the turbulent environment affects fidelity and entanglement degree in various environmental settings.

scholarly journals Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces

2015 ◽  
Vol 91 (4) ◽  
Author(s):  
David S. Simon ◽  
Casey A. Fitzpatrick ◽  
Alexander V. Sergienko
Keyword(s):  
Hilbert Spaces ◽  
Quantum States ◽  
High Dimensional

scholarly journals QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND

2011 ◽  
Vol 53 (1) ◽  
pp. 1-37 ◽  
Author(s):  
F. Y. KUO ◽  
CH. SCHWAB ◽  
I. H. SLOAN
Keyword(s):  
Monte Carlo ◽  
Hilbert Spaces ◽  
Unit Cube ◽  
High Dimensional ◽  
Equal Weight ◽  
Lattice Rules ◽  
Quasi Monte Carlo ◽  
Strong Focus ◽  
The Family ◽  
Alternative Settings

AbstractThis paper is a contemporary review of quasi-Monte Carlo (QMC) methods, that is, equal-weight rules for the approximate evaluation of high-dimensional integrals over the unit cube [0,1]s. It first introduces the by-now standard setting of weighted Hilbert spaces of functions with square-integrable mixed first derivatives, and then indicates alternative settings, such as non-Hilbert spaces, that can sometimes be more suitable. Original contributions include the extension of the fast component-by-component (CBC) construction of lattice rules that achieve the optimal convergence order (a rate of almost 1/N, where N is the number of points, independently of dimension) to so-called “product and order dependent” (POD) weights, as seen in some recent applications. Although the paper has a strong focus on lattice rules, the function space settings are applicable to all QMC methods. Furthermore, the error analysis and construction of lattice rules can be adapted to polynomial lattice rules from the family of digital nets.

Monoidal 2-Categories

2019 ◽  
pp. 265-312
Author(s):  
Chris Heunen ◽  
Jamie Vicary
Keyword(s):  
Hilbert Spaces ◽  
Two Dimensional ◽  
Monoidal Categories ◽  
Dense Coding ◽  
Graphical Calculus ◽  
Frobenius Algebras ◽  
Higher Dimensional ◽  
Modern Mathematics ◽  
Natural Way

Monoidal 2-categories are higher-dimensional versions of monoidal categories, allowing a more expressive syntax that plays an important role in modern mathematics. We explore their two-dimensional graphical calculus, and show how duality gives a language for oriented surfaces, from which Frobenius algebras emerge in a natural way. We describe 2-Hilbert spaces, categorifications of Hilbert spaces and explore the monoidal 2-category 2Hilb that they give rise to. We then show how we can use dualities in 2Hilb to give a concise and purely topological language to reason about teleportation, dense coding and complementarity.

scholarly journals Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

2021 ◽  
Author(s):  
Miguel Ángel Solís-Prosser ◽  
Omar Jiménez ◽  
Aldo Delgado ◽  
Leonardo Neves
Keyword(s):  
Hilbert Spaces ◽  
Quantum Communication ◽  
Success Probability ◽  
Quantum States ◽  
High Dimensional ◽  
Full Potential ◽  
The Core ◽  
Photonic States ◽  
Optimal Measurements ◽  
Measurement Strategies

Abstract The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identifications. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises 4- and 9-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

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