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連続変量系を用いた離散的量子情報処理

Takaya Matsuura

Published Mar 24, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.15083/0002009113

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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.
Abstract In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
Quantum information processing uses the laws of quantum physics to perform tasks that are infeasible or impossible classically. Within this broader programme, quantum communication has emerged as one of the most practically mature sub-fields of quantum information science, with several proposed protocols having already been demonstrated over deployed optical fibre and free-space links. Of the various platforms available for encoding quantum information for communication, the continuous-variable (CV) framework encodes information in the quadratures of the electromagnetic field and is therefore directly compatible with the existing machinery of classical coherent optical communications. The most prominent CV protocol is continuous-variable quantum key distribution (CV-QKD), which establishes an information-theoretically secure cryptographic key between two spatially separated parties. Because CV-QKD reuses much of the hardware of classical coherent telecommunications, including off-the-shelf lasers, modulators, and balanced detectors, it is a leading candidate for the deployment of quantum-secured communication over standard optical fibre networks. The development of CV-QKD has typically proceeded with the underlying physics dictating the engineering. Security proofs, often relying on the Gaussian optimality of collective attacks, set the structure of the protocol, and the practical system is then built to satisfy the assumptions on which those proofs depend. Contributions of this thesis adopt the opposite view, taking the practical engineering of high-rate CV-QKD systems as the starting point and developing the theoretical machinery required to support it. The first contribution is the formalisation of one-round sliced reconciliation with guard-band post-selection as a key distillation scheme designed for real-time, high-throughput operation. Originally introduced experimentally as a means to stabilise bit error rates and enable the use of fixed-rate error correction codes at high symbol rates, guard-band post-selection is shown here to identify the guard-band span as a free parameter that can be tuned to hold the quantum bit error rate approximately constant across a range of channel conditions. However, conditioning on accepted data produces non-Gaussian post-selected statistics that lie outside the reach of standard Gaussian-optimality security arguments, which motivates the remaining two contributions. The second contribution is an asymptotic security analysis of guard-band post-selected CV-QKD against arbitrary collective attacks, no longer restricted to Gaussian adversaries. By using a quantum channel estimate as side information and by lifting reduced-state distances to purification distances via entropic continuity bounds, security is certified against the class of channels lying close to a Gaussian thermal-loss reference, with a key-rate penalty that scales with the energy-constrained diamond distance to that reference. The third contribution is the experimental basis required to apply this framework in practice. A lightweight three-stage protocol for quantum channel estimation is proposed and demonstrated, which repurposes the Gaussian probe constellation already present in the CV-QKD signal and requires no additional hardware or modifications to the underlying protocol. Over single-mode optical fibre at distances from 10 km to 50 km, the protocol produces physically valid process tensor estimates whose energy-constrained diamond distances to a Gaussian reference channel remain on the order of 10^(-3) throughout. Together, these three contributions provide a treatment of post-selected Gaussian-modulated CV-QKD in which the engineering, the security theory, and the channel characterisation are designed to operate together within a deployable system.
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.
Quantum optics has been developing into a promising platform for future generation communications protocols. Much of this promise so far has come from the development of quantum key distribution (QKD). The majority of the development of QKD is done with discrete variables (DV), i.e. qubits with the underlying system of single photons. This is one interpretation of an optical field. Alternatively an optical field can be interpreted as wave with the continuous variable (CV) observables of phase and amplitude. This interpretation comes with the advantage of access to high efficiency detection at room temperature and deterministic sources at the cost of susceptibility to noise in lossy channels. This thesis presents an investigation of protocols and resources for the next generation of CV QKD protocols with two directions, the development of quantum state resources and the development of QKD protocols.This thesis starts with the details on the on going development of a low loss squeezed state resource using OPA for use in future communication and estimation experiments. So far the OPA has produced 11dB of squeezing with 13dB predicted with reasonable improvements to losses and locking. Being able to perform a Bell test with a CV Bell state is also key for future CV QKD protocols. Originally developed for DV systems the Bell test is a fundamental test of quantum mechanics. Here the first experimental demonstration of an optical CV bell test is presented. The experiment violated a CHSH Bell inequality with jBj = 2:31. This violation holds promise for being able to realise new device or source independent CV protocols. The second half of this thesis proposes a channel parameter estimation protocol based on the method of moments and presents the results of a one side device independent CV QKD demonstration based on the family of Gaussian QKD protocols. The proposed channel parameter estimation protocol through the use of the method of moments is able to use information usually disregarded for estimation of an adversaries information. The result does not allow for an increase in range of a fully optimised protocol but can increase the key rate by an order of magnitude with high loss channels. Using a newly found entroptic uncertainty relation for CV tripartite states a new security proof was applied to the family of Gaussian CV QKD protocols. This resulted in the discovery of six new protocols with the special property of being one side device independent. Using the new security proof three of the protocols were demonstrated with a positive key rate.
This thesis is concerned with the study and analysis of two quantum cryptographic protocols: quantum key distribution (QKD) and unforgeable quantum money in the continuous-variable (CV) framework. The main advantage of CV protocols is that their implementation only requires standard telecom components. QKD allows two distant parties, Alice and Bob, to establish a secure key, even in the presence of an eavesdropper, Eve. The remarkable property of QKD is that its security can be established in the information-theoretic setting, without appealing to any computational assumptions. Proving the security of CV-QKD protocols is challenging since the protocols are described in an infinite-dimensional Fock space. One of the open questions in CV-QKD was establishing security for two-way QKD protocols against general attacks. We exploit the invariance of Unitary group U(n) of the protocol to establish composable security against general attacks. We answer another pressing question in the field of CV-QKD with a discrete modulation by establishing the asymptotic security of such protocols against collective attacks. We provide a general technique to derive a lower bound on the secret key rate by formulating the problem as a semidefinite program. Quantum money exploits the no-cloning property of quantum mechanics to generate unforgeable tokens, banknotes, and credit cards. We propose a CV private-key quantum money scheme with classical verification. The motivation behind this protocol is to facilitate the process of practical implementation. Previous classical verification money schemes use single-photon detectors for verification, while our protocols use coherent detection.