Entropy

Research

16 pages, 630 KiB

Open AccessArticle

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States

by Julio A. López-Saldívar, Olga V. Man’ko, Margarita A. Man’ko and Vladimir I. Man’ko

Entropy 2023, 25(12), 1628; https://doi.org/10.3390/e25121628 - 06 Dec 2023

Viewed by 1283

The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator [...] Read more.

The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2

s u (2)

-group states) and even and odd Schrödinger cat states related to the other representation of

s u (2)

-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the

s u (2)

coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups

C_{2}

and

C_{3}

. Also, their use in quantum information and computing is mentioned. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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18 pages, 1211 KiB

Open AccessArticle

Security of the Decoy-State BB84 Protocol with Imperfect State Preparation

by Aleksei Reutov, Andrey Tayduganov, Vladimir Mayboroda and Oleg Fat’yanov

Entropy 2023, 25(11), 1556; https://doi.org/10.3390/e25111556 - 17 Nov 2023

Viewed by 965

Abstract

The quantum key distribution (QKD) allows two remote users to share a common information-theoretic secure secret key. In order to guarantee the security of a practical QKD implementation, the physical system has to be fully characterized and all deviations from the ideal protocol [...] Read more.

The quantum key distribution (QKD) allows two remote users to share a common information-theoretic secure secret key. In order to guarantee the security of a practical QKD implementation, the physical system has to be fully characterized and all deviations from the ideal protocol due to various imperfections of realistic devices have to be taken into account in the security proof. In this work, we study the security of the efficient decoy-state BB84 QKD protocol in the presence of the source flaws, caused by imperfect intensity and polarization modulation. We investigate the non-Poissonian photon-number statistics due to coherent-state intensity fluctuations and the basis-dependence of the source due to non-ideal polarization state preparation. The analysis is supported by the experimental characterization of intensity and phase distributions. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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54 pages, 8483 KiB

Open AccessArticle

Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering

by Alonso Viladomat Jasso, Ark Modi, Roberto Ferrara, Christian Deppe, Janis Nötzel, Fred Fung and Maximilian Schädler

Entropy 2023, 25(9), 1361; https://doi.org/10.3390/e25091361 - 20 Sep 2023

Viewed by 1128

Abstract

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to [...] Read more.

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed ‘quantum-inspired’ algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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12 pages, 930 KiB

Open AccessArticle

Proposal for Trapped-Ion Quantum Memristor

by Sergey Stremoukhov, Pavel Forsh, Ksenia Khabarova and Nikolay Kolachevsky

Entropy 2023, 25(8), 1134; https://doi.org/10.3390/e25081134 - 28 Jul 2023

Cited by 1 | Viewed by 1339

Abstract

A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. [...] Read more.

A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms—photonic and superconducting circuits—due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of “quantum neural networks”. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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16 pages, 994 KiB

Open AccessArticle

Fisher Information as General Metrics of Quantum Synchronization

by Yuan Shen, Hong Yi Soh, Leong-Chuan Kwek and Weijun Fan

Entropy 2023, 25(8), 1116; https://doi.org/10.3390/e25081116 - 26 Jul 2023

Viewed by 1074

Abstract

Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose [...] Read more.

Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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10 pages, 251 KiB

Open AccessArticle

Improving the Performance of Quantum Cryptography by Using the Encryption of the Error Correction Data

by Valeria A. Pastushenko and Dmitry A. Kronberg

Entropy 2023, 25(6), 956; https://doi.org/10.3390/e25060956 - 20 Jun 2023

Cited by 6 | Viewed by 1476

Abstract

Security of quantum key distribution (QKD) protocols rely solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum [...] Read more.

Security of quantum key distribution (QKD) protocols rely solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum memory after an attack despite knowing all the information disclosed during classical post-processing stages of QKD. Here, we introduce the idea of encrypting classical communication related to error-correction in order to decrease the amount of information available to the eavesdropper and hence improve the performance of quantum key distribution protocols. We analyze the applicability of the method in the context of additional assumptions concerning the eavesdropper’s quantum memory coherence time and discuss the similarity of our proposition and the quantum data locking (QDL) technique. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

9 pages, 286 KiB

Open AccessCommunication

On Constructing Informationally Complete Covariant Positive Operator-Valued Measures

by Grigori Amosov

Entropy 2023, 25(5), 783; https://doi.org/10.3390/e25050783 - 11 May 2023

Cited by 1 | Viewed by 863

Abstract

We study a projective unitary representation of the product

G = \tilde{G} \times G

, where G is a locally compact Abelian group and

\hat{G}

is its dual consisting of characters on G. It is proven that the representation is [...] Read more.

We study a projective unitary representation of the product

G = \tilde{G} \times G

, where G is a locally compact Abelian group and

\hat{G}

is its dual consisting of characters on G. It is proven that the representation is irreducible, which allows us to define a covariant positive operator-valued measure (covariant POVM) generated by orbits of projective unitary representations of

G

. The quantum tomography associated with the representation is discussed. It is shown that the integration over such a covariant POVM defines a family of contractions which are multiples of unitary operators from the representation. Using this fact, it is proven that the measure is informationally complete. The obtained results are illustrated by optical tomography on groups and by a measure with a density that has a value in the set of coherent states. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

14 pages, 13026 KiB

Open AccessArticle

Semi-Empirical Satellite-to-Ground Quantum Key Distribution Model for Realistic Receivers

by Aleksandr V. Khmelev, Egor I. Ivchenko, Alexander V. Miller, Alexey V. Duplinsky, Vladimir L. Kurochkin and Yury V. Kurochkin

Entropy 2023, 25(4), 670; https://doi.org/10.3390/e25040670 - 17 Apr 2023

Cited by 4 | Viewed by 2066

Abstract

Satellite-based link analysis is valuable for efficient and secure quantum communication, despite seasonal limits and restrictions on transmission times. A semi-empirical quantum key distribution model for satellite-based systems was proposed that simplifies simulations of communication links. Unlike other theoretical models, our approach was [...] Read more.

Satellite-based link analysis is valuable for efficient and secure quantum communication, despite seasonal limits and restrictions on transmission times. A semi-empirical quantum key distribution model for satellite-based systems was proposed that simplifies simulations of communication links. Unlike other theoretical models, our approach was based on the experimentally-determined atmospheric extinction coefficient typical for mid-latitude ground stations. The parameter was measured for both clear and foggy conditions, and it was validated using published experimental data from the Micius satellite. Using this model, we simulated secure QKD between the Micius satellite and ground stations with 300 mm and 600 mm aperture telescopes. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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13 pages, 488 KiB

Open AccessArticle

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits

by Anstasiia S. Nikolaeva, Evgeniy O. Kiktenko and Aleksey K. Fedorov

Entropy 2023, 25(2), 387; https://doi.org/10.3390/e25020387 - 20 Feb 2023

Cited by 5 | Viewed by 2170

Abstract

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to [...] Read more.

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has

O (N)

asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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15 pages, 449 KiB

Open AccessArticle

Classical Modelling of a Bosonic Sampler with Photon Collisions

by Mikhail Umanskii and Alexey N. Rubtsov

Entropy 2023, 25(2), 210; https://doi.org/10.3390/e25020210 - 21 Jan 2023

Viewed by 917

Abstract

The original formulation of the boson sampling problem assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e., the number of photons M injected into the circuit is close to the number [...] Read more.

The original formulation of the boson sampling problem assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e., the number of photons M injected into the circuit is close to the number of detectors N. Here we present a classical algorithm that simulates a bosonic sampler: it calculates the probability of a given photon distribution at the interferometer outputs for a given distribution at the inputs. This algorithm is most effective in cases with multiple photon collisions, and in those cases, it outperforms known algorithms. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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15 pages, 1382 KiB

Open AccessArticle

Suppressing Decoherence in Quantum State Transfer with Unitary Operations

by Maxim A. Gavreev, Evgeniy O. Kiktenko, Alena S. Mastiukova and Aleksey K. Fedorov

Entropy 2023, 25(1), 67; https://doi.org/10.3390/e25010067 - 30 Dec 2022

Cited by 1 | Viewed by 1708

Abstract

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical [...] Read more.

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed approach for suppressing decoherence in the process of distributing a two-qubit state over remote physical qubits of a quantum processor. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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14 pages, 712 KiB

Open AccessArticle

Asymmetric Adaptive LDPC-Based Information Reconciliation for Industrial Quantum Key Distribution

by Nikolay Borisov, Ivan Petrov and Andrey Tayduganov

Entropy 2023, 25(1), 31; https://doi.org/10.3390/e25010031 - 23 Dec 2022

Cited by 5 | Viewed by 1500

Abstract

We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme combines the advantages of LDPC codes, a priori error rate [...] Read more.

We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme combines the advantages of LDPC codes, a priori error rate estimation, rate-adaptive and blind information reconciliation techniques. We compare the performance of several asymmetric and symmetric error correction schemes using a real industrial QKD setup. The proposed asymmetric algorithm achieves significantly higher throughput, providing a secret key rate that is close to the symmetric one in a wide range of error rates. Thus, our approach is found to be particularly efficient for applications with high key rates, limited classical channel capacity and asymmetric computational resource allocation. Full article

(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)

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