Aleksey Fedorov

Quantum-secured blockchain

Blockchain is a distributed database which is cryptographically protected against malicious modifications. While promising for a wide range of applications, current blockchain platforms rely on digital signatures, which are vulnerable to attacks by means of quantum computers. The same, albeit to a lesser extent, applies to cryptographic hash functions that are used in preparing new blocks, so parties with access to quantum computation would have unfair advantage in procuring mining rewards. Here we propose a possible solution to the quantum era blockchain challenge and report an experimental realization of a quantum-safe blockchain platform that utilizes quantum key distribution across an urban fiber network for information-theoretically secure authentication. These results address important questions about realizability and scalability of quantum-safe blockchains for commercial and governmental applications.

Symmetric Blind Information Reconciliation for Quantum Key Distribution

Quantum key distribution (QKD) is a quantum-proof key-exchange scheme which is fast approaching the communication industry. An essential component in QKD is the information reconciliation step, which is used for correcting the quantum-channel noise errors. The recently suggested blind reconciliation technique, based on low-density parity-check (LDPC) codes, offers remarkable prospectives for efficient information reconciliation without an a priori error rate estimation. We suggest an improvement of the blind-information-reconciliation protocol promoting a significant increase in the efficiency of the procedure and reducing its interactivity. The proposed technique is based on introducing symmetry in operations of parties, and the consideration of results of unsuccessful belief-propagation decodings.

Post-processing procedure for industrial quantum key distribution systems

We present algorithmic solutions aimed on post-processing for industrial quantum key distribution systems with hardware sifting. The main steps of the procedure are error correction, parameter estimation, and privacy amplification. Authentication of a classical public communication channel is also considered.

Tomography of a multimode quantum black box

We report a technique for experimental characterization of an M-mode quantum optical process, generalizing the single-mode coherent-state quantum-process tomography method [1, 2]. By measuring the effect of the process on multi-mode coherent states via balanced homodyne tomography, we obtain the process tensor in the Fock basis. This rank- tensor, which predicts the effect of the process on an arbitrary density matrix, is iteratively reconstructed directly from the experimental data via the maximum-likelihood method. We demonstrate the capabilities of our method using the example of a beam splitter, reconstructing its process tensor within the subspace spanned by the first three Fock states. In spite of using purely classical probe states, we recover quantum properties of this optical element, in particular the Hong–Ou–Mandel effect.

Note: Gaussian mixture model for event recognition in optical time-domain reflectometry based sensing systems.

We propose a novel approach to the recognition of particular classes of non-conventional events in signals from phase-sensitive optical time-domain-reflectometry-based sensors. Our algorithmic solution has two main features: filtering aimed at the de-nosing of signals and a Gaussian mixture model to cluster them. We test the proposed algorithm using experimentally measured signals. The results show that two classes of events can be distinguished with the best-case recognition probability close to 0.9 at sufficient numbers of training samples.

Structural monitoring system with fiber Bragg grating sensors: implementation and software solution

We present a structural health monitoring system for nondestructive testing of composite materials based on the fiber Bragg grating sensors and specialized software solution. The developed structural monitoring system has potential applications for preliminary tests of novel composite materials as well as real-time structural health monitoring of industrial objects. The software solution realizes control for the system, data processing, and alert of an operator.

Tomographic causal analysis of two-qubit states and tomographic discord

Abstract We study a behavior of two-qubit states subject to tomographic measurement. In this Letter we propose a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies. We consider two types of measurement bases: the first is one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second is one that maximizes Shannon mutual information and relates to symmetrical form quantum discord. We show how these approaches relate to each other and then implement them to the different classes of two-qubit states. Consequently, new subclasses of X-states are revealed.

Quaternion Representation and Symplectic Spin Tomography

Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In the tomographic description of spin states, the connection between special unitary and special orthogonal groups is used. We analyze the representation for spin tomography using the Cayley–Klein parameters and discuss an analog of symplectic tomography for discrete variables. We propose a representation for tomograms of discrete variables through quaternions and employ the qubit-state tomogram to illustrate the method elaborated.

Motion of a system of oscillators under the generalized dry friction control

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to equilibrium. The problem of existence and uniqueness of motion under the suggested control is resolved within the framework of the DiPerna-Lions theory of singular ordinary differential equations.

Asymptotic Control Theory for a Closed String

We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit complete damping and an asymptotically exact value of the required time. By using approximate reachable sets instead of exact ones, we design a dry-friction like feedback control, which turns out to be asymptotically optimal. We prove the existence of motion under the control using a rather explicit solution of a nonlinear wave equation. Remarkably, the solution is determined via purely algebraic operations. The main result is a proof of asymptotic optimality of the control thus constructed.