Related papers: An Iterative Methodology for Unitary Quantum Chann…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
We test a general method to detect lower bounds of the quantum channel capacity for two-qubit correlated channels. We consider in particular correlated dephasing, depolarising and amplitude damping channels. We show that the method is…
Designing a mixed quantum channel is challenging due to the complexity of the transformations and the probabilistic mixtures of more straightforward channels involved. Fully characterizing a quantum channel generally requires preparing a…
In this paper we use the method of a recent paper (quant-ph/0509101) to compute complementary channels for certain important cases, such as depolarizing and transpose-depolarizing channels. This method allows us to easily obtain the minimal…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…
In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the…
Random (mixed) unitary channels describe an important subset of quantum channels, which are commonly used in quantum information, noise modeling, and quantum error mitigation. Despite their usefulness, there is substantial complexity in…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their…
The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown…
We derive a general criterion to detect entangled states in multi-partite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…
An arbitrary lossless transformation in high-dimensional quantum space can be decomposed into elementary operations which are easy to implement, and an effective decomposition algorithm is important for constructing high-dimensional…
We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…