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9 pages, 385 KiB

Open AccessArticle

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing

by Xiaoming Chen, Lei Chen and Yalong Yan

Entropy 2022, 24(9), 1232; https://doi.org/10.3390/e24091232 - 02 Sep 2022

Viewed by 1656

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols [...] Read more.

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user’s pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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12 pages, 2776 KiB

Open AccessFeature PaperArticle

Entanglement-Assisted Joint Monostatic-Bistatic Radars

by Ivan B. Djordjevic

Entropy 2022, 24(6), 756; https://doi.org/10.3390/e24060756 - 26 May 2022

Cited by 6 | Viewed by 1783

Abstract

With the help of entanglement, we can build quantum sensors with sensitivity better than that of classical sensors. In this paper we propose an entanglement assisted (EA) joint monostatic-bistatic quantum radar scheme, which significantly outperforms corresponding conventional radars. The proposed joint monostatic-bistatic quantum [...] Read more.

With the help of entanglement, we can build quantum sensors with sensitivity better than that of classical sensors. In this paper we propose an entanglement assisted (EA) joint monostatic-bistatic quantum radar scheme, which significantly outperforms corresponding conventional radars. The proposed joint monostatic-bistatic quantum radar is composed of two radars, one having both wideband entangled source and EA detector, and the second one with only an EA detector. The optical phase conjugation (OPC) is applied on the transmitter side, while classical coherent detection schemes are applied in both receivers. The joint monostatic-bistatic integrated EA transmitter is proposed suitable for implementation in LiNbO₃ technology. The detection probability of the proposed EA joint target detection scheme outperforms significantly corresponding classical, coherent states-based quantum detection, and EA monostatic detection schemes. The proposed EA joint target detection scheme is evaluated by modelling the direct radar return and forward scattering channels as both lossy and noisy Bosonic channels, and assuming that the distribution of entanglement over idler channels is not perfect. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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24 pages, 8050 KiB

Open AccessArticle

Error Performance of Amplitude Shift Keying-Type Asymmetric Quantum Communication Systems

by Tiancheng Wang and Tsuyoshi Sasaki Usuda

Entropy 2022, 24(5), 708; https://doi.org/10.3390/e24050708 - 16 May 2022

Cited by 1 | Viewed by 1991

Abstract

We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using [...] Read more.

We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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10 pages, 11666 KiB

Open AccessArticle

Non-Orthogonality Measure for a Collection of Pure Quantum States

by Kentaro Kato

Entropy 2022, 24(5), 581; https://doi.org/10.3390/e24050581 - 21 Apr 2022

Cited by 4 | Viewed by 1579

Abstract

Modern optical communication technology can realize a large-scale multilevel (or M-ary) optical signal. Investigating the quantum mechanical nature of such a large-scale M-ary optical signal is essential for a unified understanding of quantum information science and optical communication technology. This article [...] Read more.

Modern optical communication technology can realize a large-scale multilevel (or M-ary) optical signal. Investigating the quantum mechanical nature of such a large-scale M-ary optical signal is essential for a unified understanding of quantum information science and optical communication technology. This article focuses on the quantum-mechanical non-orthogonality for a collection of pure quantum states and proposes a non-orthogonality index based on the least squares error criterion in quantum detection theory. First, we define the index for linearly independent signals, and the proposed index is analyzed through numerical simulations. Next, the index is applied to a highly large-scale M-ary phase-shift keying (PSK) coherent state signal. Furthermore, the index is compared with the capacity of the pure state channel with the PSK signal. As a result, it is shown that a highly large-scale M-ary PSK coherent state signal exhibits a quantum nature even when the signal transmission power is very high. Thus, the theoretical characterization of a highly large-scale M-ary coherent state signal based on the proposed index will be the first step toward a better understanding of cutting-edge optical communication technologies such as the quantum stream cipher Y00. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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17 pages, 432 KiB

Open AccessArticle

Simplification of the Gram Matrix Eigenvalue Problem for Quadrature Amplitude Modulation Signals

by Ryusuke Miyazaki, Tiancheng Wang and Tsuyoshi Sasaki Usuda

Entropy 2022, 24(4), 544; https://doi.org/10.3390/e24040544 - 13 Apr 2022

Cited by 2 | Viewed by 2293

Abstract

In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the upper and lower bounds of [...] Read more.

In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the upper and lower bounds of the reliability function. Solving the eigenvalue problem also provides a matrix representation of quantum signals, which is useful for simulating quantum systems. In the case of symmetric signals, analytic solutions to the eigenvalue problem of the Gram matrix have been obtained, and efficient computations are possible. However, for asymmetric signals, there is no analytic solution and universal numerical algorithms that must be used, rendering the computations inefficient. Recently, we have shown that, for asymmetric signals such as amplitude-shift keying coherent-state signals, the Gram matrix eigenvalue problem can be simplified by exploiting its partial symmetry. In this paper, we clarify a method for simplifying the eigenvalue problem of the Gram matrix for quadrature amplitude modulation (QAM) signals, which are extremely important for applications in quantum communication and quantum ciphers. The results presented in this paper are applicable to ordinary QAM signals as well as modified QAM signals, which enhance the security of quantum cryptography. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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10 pages, 401 KiB

Open AccessArticle

Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory

by Yves Pomeau and Martine Le Berre

Entropy 2021, 23(12), 1643; https://doi.org/10.3390/e23121643 - 07 Dec 2021

Cited by 2 | Viewed by 1872

Abstract

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant [...] Read more.

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general “kinetic Kolmogorov-like” equation for the evolution of the probability. In the simple case considered here, the probability only depends on a single variable

θ

describing the state of the atom, and

p (θ, t)

yields the statistical properties of the atom under the joint effects of coherent pumping and random emission of photons. We emphasize that

p (θ, t)

allows the description of all possible histories of the atom, as in Everett’s many-worlds interpretation of quantum mechanics. This yields solvable equations in the two-level atom case. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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12 pages, 355 KiB

Open AccessArticle

A Method to Compute the Schrieffer–Wolff Generator for Analysis of Quantum Memory

by Dong-Hwan Kim, Su-Yong Lee, Yonggi Jo, Duk Y. Kim, Zaeill Kim and Taek Jeong

Entropy 2021, 23(10), 1260; https://doi.org/10.3390/e23101260 - 27 Sep 2021

Viewed by 1551

Abstract

Quantum illumination uses entangled light that consists of signal and idler modes to achieve higher detection rate of a low-reflective object in noisy environments. The best performance of quantum illumination can be achieved by measuring the returned signal mode together with the idler [...] Read more.

Quantum illumination uses entangled light that consists of signal and idler modes to achieve higher detection rate of a low-reflective object in noisy environments. The best performance of quantum illumination can be achieved by measuring the returned signal mode together with the idler mode. Thus, it is necessary to prepare a quantum memory that can keep the idler mode ideal. To send a signal towards a long-distance target, entangled light in the microwave regime is used. There was a recent demonstration of a microwave quantum memory using microwave cavities coupled with a transmon qubit. We propose an ordering of bosonic operators to efficiently compute the Schrieffer–Wolff transformation generator to analyze the quantum memory. Our proposed method is applicable to a wide class of systems described by bosonic operators whose interaction part represents a definite number of transfer in quanta. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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14 pages, 326 KiB

Open AccessEditor’s ChoiceArticle

On the Classical Capacity of General Quantum Gaussian Measurement

by Alexander Holevo

Entropy 2021, 23(3), 377; https://doi.org/10.3390/e23030377 - 21 Mar 2021

Cited by 6 | Viewed by 2349

Abstract

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we [...] Read more.

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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Review

Jump to: Research

15 pages, 3217 KiB

Open AccessReview

Quantum Stream Cipher Based on Holevo–Yuen Theory

by Masaki Sohma and Osamu Hirota

Entropy 2022, 24(5), 667; https://doi.org/10.3390/e24050667 - 10 May 2022

Cited by 2 | Viewed by 2274

Abstract

In this review paper, we first introduce the basic concept of quantum computer-resistant cryptography, which is the cornerstone of security technology for the network of a new era. Then, we will describe the positioning of mathematical cryptography and quantum cryptography, that are currently [...] Read more.

In this review paper, we first introduce the basic concept of quantum computer-resistant cryptography, which is the cornerstone of security technology for the network of a new era. Then, we will describe the positioning of mathematical cryptography and quantum cryptography, that are currently being researched and developed. Quantum cryptography includes QKD and quantum stream cipher, but we point out that the latter is expected as the core technology of next-generation communication systems. Various ideas have been proposed for QKD quantum cryptography, but most of them use a single-photon or similar signal. Then, although such technologies are applicable to special situations, these methods still have several difficulties to provide functions that surpass conventional technologies for social systems in the real environment. Thus, the quantum stream cipher has come to be expected as one promising countermeasure, which artificially creates quantum properties using special modulation techniques based on the macroscopic coherent state. In addition, it has the possibility to provide superior security performance than one-time pad cipher. Finally, we introduce detailed research activity aimed at putting the quantum stream cipher into practical use in social network technology. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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17 pages, 311 KiB

Open AccessFeature PaperReview

Introduction to Semi-Classical Analysis for Digital Errors of Qubit in Quantum Processor

by Osamu Hirota

Entropy 2021, 23(12), 1577; https://doi.org/10.3390/e23121577 - 26 Nov 2021

Cited by 1 | Viewed by 1571

Abstract

In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has [...] Read more.

In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has been pointed out that a new type of quantum error, such as nonlinear error, appears. It is not clear how to handle such new effects in information theory. First of all, one should make the characteristics of the error probability of qubits clear as communication channel error models in information theory. The purpose of this paper is to survey the progress for modeling the quantum noise effects that information theorists are likely to face in the future, to cope with such nontrivial errors mentioned above. This paper explains a channel error model to represent strange properties of error probability due to new quantum noise. By this model, specific examples on the features of error probability caused by, for example, quantum recurrence effects, collective relaxation, and external force, are given. As a result, it is possible to understand the meaning of strange features of error probability that do not exist in classical information theory without going through complex physical phenomena. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)

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