The quantum version of the linearization theorem

2002 ◽  
pp. 119-137
Author(s):  
Victor Guillemin ◽  
Viktor Ginzburg ◽  
Yael Karshon
Keyword(s):  
Linearization Theorem ◽  
Quantum Version

scholarly journals An alternative proof of Lie’s linearization theorem using a new λ-symmetry criterion

2015 ◽  
Vol 26 (1-3) ◽  
pp. 45-51
Author(s):  
Ahmad Y. Al-Dweik ◽  
M.T. Mustafa ◽  
Raed A. Mara’Beh ◽  
F.M. Mahomed
Keyword(s):  
Alternative Proof ◽  
Linearization Theorem ◽  
Symmetry Criterion

scholarly journals From Quantum Groups to Groups

2013 ◽  
Vol 65 (5) ◽  
pp. 1073-1094 ◽  
Author(s):  
Mehrdad Kalantar ◽  
Matthias Neufang
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Locally Compact ◽  
Large Classes ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Recent Developments ◽  
Compact Quantum Groups ◽  
Quantum Version ◽  
Quantum Point

AbstractIn this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign to each locally compact quantum group 𝔾 a locally compact group 𝔾˜ that is the quantum version of point-masses and is an invariant for the latter. We show that “quantum point-masses” can be identified with several other locally compact groups that can be naturally assigned to the quantum group 𝔾. This assignment preserves compactness as well as discreteness (hence also finiteness), and for large classes of quantum groups, amenability. We calculate this invariant for some of the most well-known examples of non-classical quantum groups. Also, we show that several structural properties of 𝔾 are encoded by 𝔾˜; the latter, despite being a simpler object, can carry very important information about 𝔾.

scholarly journals Quantum Free-Start Collision Attacks on Double Block Length Hashing with Round-Reduced AES-256

2021 ◽  
pp. 316-336
Author(s):  
Amit Kumar Chauhan ◽  
Abhishek Kumar ◽  
Somitra Kumar Sanadhya
Keyword(s):  
Time Complexity ◽  
Block Length ◽  
Compression Function ◽  
Collision Attack ◽  
Classical Setting ◽  
Quantum Version ◽  
Collision Attacks ◽  
Double Block Length

Recently, Hosoyamada and Sasaki (EUROCRYPT 2020), and Xiaoyang Dong et al. (ASIACRYPT 2020) proposed quantum collision attacks against AES-like hashing modes AES-MMO and AES-MP. Their collision attacks are based on the quantum version of the rebound attack technique exploiting the differential trails whose probabilities are too low to be useful in the classical setting but large enough in the quantum setting. In this work, we present dedicated quantum free-start collision attacks on Hirose’s double block length compression function instantiated with AES-256, namely HCF-AES-256. The best publicly known classical attack against HCF-AES-256 covers up to 9 out of 14 rounds. We present a new 10-round differential trail for HCF-AES-256 with probability 2−160, and use it to find collisions with a quantum version of the rebound attack. Our attack succeeds with a time complexity of 285.11 and requires 216 qRAM in the quantum-attack setting, where an attacker can make only classical queries to the oracle and perform offline computations. We also present a quantum free-start collision attack on HCF-AES-256 with a time complexity of 286.07 which outperforms Chailloux, Naya-Plasencia, and Schrottenloher’s generic quantum collision attack (ASIACRYPT 2017) in a model when large qRAM is not available.

Conservation laws in the quantum version ofN-positional Potts model

1980 ◽  
Vol 76 (2) ◽  
pp. 129-141 ◽  
Author(s):  
Yu. A. Bashilov ◽  
S. V. Pokrovsky
Keyword(s):  
Conservation Laws ◽  
Potts Model ◽  
Quantum Version
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