Digital Quantum Information Processing with Continuous-Variable Systems

Philippe Grangier

Takaya Matsuura

Continuous-variable quantum systems are characterized by physical quantities that can take continuous values.It appears in many physical systems, such as the position and momentum of oscillator modes of trapped ions and the complex amplitude of an optical mode.Especially, the quantum optical system is one of the most important continuous-variable systems for the quantum information application since light is an information carrier for telecommunication and behaves quantum mechanically even in the room-temperature environment.Furthermore, the complex amplitude of the optical mode can easily be manipulated.However, using a continuous variable, as it is, in quantum information processing does not work since a continuous variable is subject to continuous noises in the physical world, and such noises cannot completely be corrected.In order to perform reliable and fault-tolerant quantum information processing, information should be encoded in a digitized degree of freedom.In this thesis, digital quantum information processing with continuous-variables systems is studied in the quantum key distribution (QKD) and the quantum computation (QC), two major fields of quantum information processing.For the QKD, the so-called continuous-variable QKD protocols, in which information is encoded on the complex amplitude of an optical pulse and the homodyne or heterodyne detector is used to measure it, are studied.More specifically, a continuousvariable QKD protocol that uses discretely modulated signals and the classical digital information processing is developed, and its security proof against general attacks in the finite-key case is established.This is achieved by virtually introducing the discretevariable quantum system into the continuous-variable system and thereby reducing its security argument to that of discrete-variable QKDs, which is more mature.This is in sharp contrast to the previous security analyses on this kind of QKD protocol, where they directly use continuous variables in the security analyses and thus have difficulty in extending the analyses to the finite-key case.Another key to our security proof is the development of the method of estimating a lower bound on the fidelity to the coherent states, which eventually leads to the evaluation of how well the discrete-variable system can be approximated by the continuous-variable one.These security analyses are further elaborated, and a protocol whose key rate against the loss noise achieves almost optimal scaling is obtained.For the QC with the continuous-variable system, the Gottesman-Kitaev-Preskill (GKP) code, which encodes discrete quantum information into a continuous-variable system, is studied.This code has many desirable properties for the optical implementation of QC; e.g., the universal QC is possible using only the Gaussian operations, which are relatively easy to implement in the quantum optical system, along with the GKP-encoded states.Because the ideal GKP-encoded state is unphysical, only i I have received much support and advice during my Ph.D. studies.First, I would like to express my sincere thanks to my supervisor Masato Koashi for the instruction and all the constructive suggestions.He was always ready to listen to my questions and concerns for both academic and non-academic matters.From him, I learned the approaches to challenging problems and the importance of thorough consideration.

Takaya Matsuura

Cumali Yaşar, Can Aktaş

Ensuring the security of digital communication and data transfer has become essential in the modern era. Classical cryptographic techniques are increasingly vulnerable due to advances in quantum technologies and algorithms. Consequently, quantum computers and quantum communication offer promising solutions for secure data transfer and encryption. This study explores the generation of Quantum Digital Signatures (QDS) using Quantum Continuous Variables (QCV), providing a novel approach to secure digital signature technologies. The paper outlines the core principles of QDS generation with QCV, detailing the signature creation and verification processes. It highlights the advantages of this technology in secure communication and data transfer and discusses potential security vulnerabilities and future development prospects. Quantum Continuous Variables (QCVs), typically used in quantum optical systems, represent physical quantities with continuous spectra, such as the wavelength or phase of light. These variables enable efficient and secure quantum information processing and communication. Despite significant progress in quantum cryptography protocols using QCVs, practical application and optimization of these technologies face numerous challenges. These include complexities in preparing and measuring quantum states, managing quantum errors, and achieving higher efficiency and security standards. Moreover, the practical applications of QCV in industrial contexts remain limited, highlighting the need for further experimental and applied research. The methodology for generating QDS using QCVs involves employing specific quantum states, such as coherent and squeezed states. The process includes key distribution, signature creation and verification, and addressing potential quantum attacks. The system model comprises a sender (Alice), a receiver (Bob), and an arbiter (Charlie), facilitating secure and authenticated message transmission.

Yuan Liu, John M. Martyn, Jasmine Sinanan-Singh +3 more

Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leverageddigitalquantum resources, such as discrete-variable (DV) systems like qubits, rather thananalogquantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals— specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.

Christian Weedbrook, Bhaskar Roy Bardhan