Searcharxiv⌕ Search

arXiv subjects

Minhyung Cho

Publications and source records attributed to Minhyung Cho.

7 recordsLinked to original sources
arXiv2022

The Local Orthogonality between Quantum States and Entanglement Decomposition

In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki [Acta Phys. Slov. 48, 141 (1998).]. But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence.

quant-ph↗
arXiv2019

The geometry properties of parity and time reversal operators in two dimensional spaces

The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss their geometrical properties in two dimensional spaces. It is showed that if $\cal T$ is given, then all $\cal P$ links with the quadric surfaces; if $\cal P$ is given, then all $\cal T$ links with the quadric curves. Moreover, we give out the generalized unbroken $\cal PT$-symmetric condition of an operator. The unbroken $\cal PT$-symmetry of a Hermitian operator is also showed in this way.

quant-ph↗
arXiv2018

Exeum: A Decentralized Financial Platform for Price-Stable Cryptocurrencies

Price stability has often been cited as a key reason that cryptocurrencies have not gained widespread adoption as a medium of exchange and continue to prove incapable of powering the economy of decentralized applications (DApps) efficiently. Exeum proposes a novel method to provide price stable digital tokens whose values are pegged to real world assets, serving as a bridge between the real world and the decentralized economy. Pegged tokens issued by Exeum - for example, USDE refers to a stable token issued by the system whose value is pegged to USD - are backed by virtual assets in a virtual asset exchange where users can deposit the base token of the system and take long or short positions. Guaranteeing the stability of the pegged tokens boils down to the problem of maintaining the peg of the virtual assets to real world assets, and the main mechanism used by Exeum is controlling the swap rate of assets. If the swap rate is fully controlled by the system, arbitrageurs can be incentivized enough to restore a broken peg; Exeum distributes statistical arbitrage trading software to decentralize this type of market making activity. The last major component of the system is a central bank equivalent that determines the long term interest rate of the base token, pays interest on the deposit by inflating the supply if necessary, and removes the need for stability fees on pegged tokens, improving their usability. To the best of our knowledge, Exeum is the first to propose a truly decentralized method for developing a stablecoin that enables 1:1 value conversion between the base token and pegged assets, completely removing the mismatch between supply and demand. In this paper, we will also discuss its applications, such as improving staking based DApp token models, price stable gas fees, pegging to an index of DApp tokens, and performing cross-chain asset transfer of legacy crypto assets.

cs.CR↗
arXiv2018

Field extension of real values of physical observables in classical theory can help attain quantum results

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what will happen if physical observables are allowed to take complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.

quant-ph↗
arXiv2017

Riemannian approach to batch normalization

Batch Normalization (BN) has proven to be an effective algorithm for deep neural network training by normalizing the input to each neuron and reducing the internal covariate shift. The space of weight vectors in the BN layer can be naturally interpreted as a Riemannian manifold, which is invariant to linear scaling of weights. Following the intrinsic geometry of this manifold provides a new learning rule that is more efficient and easier to analyze. We also propose intuitive and effective gradient clipping and regularization methods for the proposed algorithm by utilizing the geometry of the manifold. The resulting algorithm consistently outperforms the original BN on various types of network architectures and datasets.

cs.LG↗
arXiv2015

Hessian-free Optimization for Learning Deep Multidimensional Recurrent Neural Networks

Multidimensional recurrent neural networks (MDRNNs) have shown a remarkable performance in the area of speech and handwriting recognition. The performance of an MDRNN is improved by further increasing its depth, and the difficulty of learning the deeper network is overcome by using Hessian-free (HF) optimization. Given that connectionist temporal classification (CTC) is utilized as an objective of learning an MDRNN for sequence labeling, the non-convexity of CTC poses a problem when applying HF to the network. As a solution, a convex approximation of CTC is formulated and its relationship with the EM algorithm and the Fisher information matrix is discussed. An MDRNN up to a depth of 15 layers is successfully trained using HF, resulting in an improved performance for sequence labeling.

cs.LG↗