Arbitrary classical privicy amplification can be used for the quantum key distribution

Stream privacy amplification for quantum cryptography

Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated before privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy amplification scheme, which resembles t…

On the role of dealing with quantum coherence in amplitude amplification

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence …

Noise powered amplification in CV quantum key distribution

Amplification plays a key role in classical communication protocols, where it compensates the unavoidable loss of the signal. However, when we enter the quantum domain this approach starts being problematic as the standard kinds of amplifiers are usually accompanied by excess noise which detrimentally affects the quantum features of used states. Recently, several kinds of "noiseless" amplifiers that do not suffer from this feature have been proposed. Among these amplifiers, one that stands out is the noise powered amplifier, which acts incoherently, amplifying the signal by adding the "right" …

Privacy Amplification, Private States, and the Uncertainty Principle

We show that three principle means of treating privacy amplification in quantum key distribution, private state distillation, classical privacy amplification, and via the uncertainty principle, are equivalent and interchangeable. By adapting the security proof based on the uncertainty principle, we construct a new protocol for private state distillation which we prove is identical to standard classical privacy amplification. Underlying this approach is a new characterization of private states, related to their standard formulation by the uncertainty principle, which gives a more physical under…

Quantum key distribution with delayed privacy amplification and its application to security proof of a two-way deterministic protocol

Privacy amplification (PA) is an essential post-processing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate…

Universally composable privacy amplification against quantum adversaries

Privacy amplification is the art of shrinking a partially secret string Z to a highly secret key S. We show that, even if an adversary holds quantum information about the initial string Z, the key S obtained by two-universal hashing is secure, according to a universally composable security definition. Additionally, we give an asymptotically optimal lower bound on the length of the extractable key S in terms of the adversary's (quantum) knowledge about Z. Our result has applications in quantum cryptography. In particular, it implies that many of the known quantum key distribution protocols are …

分布式精确量子振幅放大算法用于任意量子态

Distributed Exact Quantum Amplitude Amplification Algorithm for Arbitrary Quantum States

本文提出分布式精确量子振幅放大算法，通过分解C^{n-1}PS门实现对任意量子态的多目标精确振幅放大，显著提升噪声容忍度和资源利用效率。

Large-scale and High-speed Privacy Amplification for FPGA-based Quantum Key Distribution

The FPGA-based Quantum key distribution (QKD) system is an important trend of QKD systems. It has several advantages, real time, low power consumption and high integration density. Privacy amplification is an essential part in a QKD system to ensure the security of QKD. Existing FPGA-based privacy amplification schemes have an disadvantage, that the throughput and the input size of these schemes (the best scheme 116Mbps@10^6) are much lower than these on other platforms (the best scheme 1Gbps@10^8). This paper designs a new PA scheme for FPGA-based QKD with multilinear modular hash-modular ari…

High-speed Implementation of FFT-based Privacy Amplification on FPGA in Quantum Key Distribution

Privacy amplification (PA) is a vital procedure in quantum key distribution (QKD) to generate the secret key that the eavesdropper has only negligible information from the identical correcting key for the communicating parties. With the increase of repeat frequency of discrete-variable QKD (DV-QKD) system, the processing speed of PA has become the bottle neck restricting DV-QKD's secure key rate. The PA using Toeplitz-based Hash function is adopted widely because of its simplicity and parallel feature. Because this algorithm can be accelerated with Fast Fourier Transform (FFT), an improved sch…

Proposal for Implementing Device-Independent Quantum Key Distribution based on a Heralded Qubit Amplification

In device-independent quantum key distribution (DIQKD), the violation of a Bell inequality is exploited to establish a shared key that is secure independently of the internal workings of the QKD devices. An experimental implementation of DIQKD, however, is still awaited, since hitherto all optical Bell tests are subject to the detection loophole, making the protocol unsecured. In particular, photon losses in the quantum channel represent a fundamental limitation for DIQKD. Here, we introduce a heralded qubit amplifier based on single-photon sources and linear optics that provides a realistic s…

Exploiting the randomness of the measurement basis in quantum cryptography: Secure Quantum Key Growing without Privacy Amplification

We suggest that the randomness of the choices of measurement basis by Alice and Bob provides an additional important resource for quantum cryptography. As a specific application, we present a novel protocol for quantum key distribution (QKD) which enhances the BB84 scheme by encrypting the information sent over the classical channel during key sifting. We show that, in the limit of long keys, this process prevents an eavesdropper from reproducing the sifting process carried out by the legitimate users. The inability of the eavesdropper to sift the information gathered by tapping the quantum ch…

Secure bound analysis of quantum key distribution with non-uniform random seed of privacy amplification

Precise quantum key distribution (QKD) secure bound analysis is essential for practical QKD systems. The effect of uniformity of random number seed for privacy amplification is not considered in existing secure bound analysis. In this paper, we propose and prove the quantum leftover hash lemma with non-uniform random number seeds based on the min-entropy, and we give a precise QKD secure bound analysis with non-uniform random number seeds on this basis. We take the two-decoy BB84 protocol as an example to simulate the effect of random number seed uniformity on the secure bound of a QKD system.…

充分利用剩余资源：量子密钥分发的改进隐私放大

Making the most of leftovers: Improved privacy amplification for quantum key distribution

本文通过细化Regula和Tomamichel的剩余哈希引理，改进量子密钥分发的隐私放大界，在有限块体制下从相同实验数据中提取更多密钥，优于熵累积技术。

Multi-mode CV-QKD with Noiseless Attenuation and Amplification

In this work we study the use of noiseless attenuation and noiseless amplification, in terms of multi-mode Continuous-Variable (CV) Quantum Key Distribution (QKD) over satellite-to-ground channels. We propose an improved multi-mode CV-QKD protocol where noiseless attenuation and noiseless amplification operations are applied at the transmitter and the receiver, respectively. Our results show that consistent with single-mode CV-QKD, the noiseless amplification operation, when applied at the receiver, can increase the transmission distance and the channel noise tolerance of multi-mode CV-QKD. Di…

任意本征态和多输出的量子纯度放大

Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs

本文研究了在任意本征态和多输出情况下量子纯度放大的问题，提出了最优通道的特性，并推导了其在不同输出区域的性能规律，同时给出了非渐近分析中的通用杨表理论，提供了最优QPA的紧样本复杂度界和首次维度均匀保证。

量子密钥分发中错误验证与隐私放大的结合

Combining Error Verification and Privacy Amplification in Quantum Key Distribution

本研究针对量子密钥分发协议，提出将错误验证与隐私放大合并为单步哈希过程的方案，证明其在密钥率不变、安全参数微调下可保证安全性，能降低经典后处理等的复杂度与资源需求。

利用误差放大实现任意角度单量子比特门的驱动非线性校准

Calibration of Drive Non-Linearity for Arbitrary-Angle Single-Qubit Gates Using Error Amplification

针对控制线非线性组件导致的单量子比特门性能受限问题，提出基于误差放大的驱动非线性校准方法，校正后任意角度单量子比特门误差达相干极限，该方法适用于各类非线性来源。

Squeezing arbitrary cavity-field states through their interaction with a single driven atom

We propose an implementation of the parametric amplification of an arbitrary radiation-field state previously prepared in a high-Q cavity. This nonlinear process is accomplished through the dispersive interactions of a single three-level atom (fundamental |g>, intermediate |i>, and excited |e> levels) simultaneously with i) a classical driving field and ii) a previously prepared cavity mode whose state we wish to squeeze. We show that, in the adiabatic approximantion, the preparation of the initial atomic state in the intermediate level |i> becomes crucial for obtaing the degenerated parametri…

Deterministic noiseless amplification of coherent states

A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum state transformation, we show that deterministic noiseless amplification of coherent states chosen from a proper set is possible. The relation between input coherent states and gain of amplification for deterministic noiseless amplification is thus derived. Besides, the potential applications of amplification of coherent states in quantum key distribution (QKD)…

Extension of the input-output relation for a Michelson interferometer to arbitrary coherent-state light sources: --- Gravitational-wave detector and weak-value amplification ---

An extension of the input-output relation for a conventional Michelson interferometric gravitational-wave detector is carried out to treat an arbitrary coherent state for the injected optical beam. This extension is one of necessary researches toward the clarification of the relation between conventional gravitational-wave detectors and a simple model of a gravitational-wave detector inspired by weak-measurements in [A.~Nishizawa, Phys. Rev. A {\bf 92} (2015), 032123.]. The derived input-output relation describes not only a conventional Michelson-interferometric gravitational-wave detector but…

任意时间轮廓的时间变化介质中的量子真空放大

Quantum vacuum amplification in time-varying media with arbitrary temporal profiles

本文提出基于共轭谐振子的理论框架，研究任意时间调制轮廓下时间变化介质中的量子真空放大效应，发现最快最强调制并非最优，为设计增强量子现象的时间调制序列提供关键见解。

A QKD Protocol Extendable to Support Entanglement and Reduce Unauthorized Information Gain by Randomizing the Bases Lists with Key Values and Invalidate Explicit Privacy Amplification

This paper suggests an improvement to the BB84 scheme in Quantum key distribution. The original scheme has its weakness in letting quantifiably more information gain to an eavesdropper during public announcement of unencrypted bases lists. The security of the secret key comes at the expense of the final key length. We aim at exploiting the randomness of preparation (measurement) basis and the bit values encoded (observed), so as to randomize the bases lists before they are communicated over the public channel. A proof of security is given for our scheme and proven that our protocol results in …

Method for decoupling error correction from privacy amplification

Entanglement purification provides a unifying framework for proving the security of quantum key distribution schemes. Nonetheless, up till now, a local commutability constraint in the CSS code construction means that the error correction and privacy amplification procedures of BB84 are not fully decoupled. Here, I provide a method to decouple the two processes completely. The method requires Alice and Bob to share some initial secret string and use it to encrypt the bit-flip error syndrome using one-time-pad encryption. As an application, I prove the unconditional security of the interactive C…

Effective Privacy Amplification for Secure Classical Communications

We study the practical effectiveness of privacy amplification for classical key-distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key-bits. The number of privacy amplification iterations needed to achieve information leak of 10^-8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff b…

面向量子密钥分发的基于FPGA的大规模隐私放大方案，支持超过$10^8$比特

Large-Scale FPGA-Based Privacy Amplification Exceeding $10^8$ Bits for Quantum Key Distribution

本文提出并实现了一种基于FPGA的大规模隐私放大方案，支持超过$10^8$比特的输入输出规模，通过新算法显著缓解QKD中的有限尺寸效应并提升安全密钥率。

Privacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound

In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the point…

High-speed Privacy Amplification Scheme using GMP in Quantum Key Distribution

Privacy amplification (PA) is the art of distilling a highly secret key from a partially secure string by public discussion. It is a vital procedure in quantum key distribution (QKD) to produce a theoretically unconditional secure key. The throughput of PA has become a bottleneck of the high-speed discrete variable QKD (DV-QKD) system. In this paper, a high-speed modular arithmetic hash PA scheme with GNU multiple precision (GMP) arithmetic library is presented. This scheme is implemented on two different central processing unit (CPU) platforms. The experimental results demon-strate that the t…

Noise Tolerance of the BB84 Protocol with Random Privacy Amplification

We prove that BB84 protocol with random privacy amplification is secure with a higher key rate than Mayers' estimate with the same error rate. Consequently, the tolerable error rate of this protocol is increased from 7.5 % to 11 %. We also extend this method to the case of estimating error rates separately in each basis, which enables us to securely share a longer key.

使用量子隐私放大克服QKD中的噪声限制

Overcoming Noise Limitations in QKD with Quantum Privacy Amplification

本文实验证明量子隐私放大（QPA）通过提升分布式纠缠质量，有效提高QKD安全密钥率，并能在高噪声下生成密钥，为全球量子网络奠定基础。

An efficient hybrid hash based privacy amplification algorithm for quantum key distribution

Privacy amplification (PA) is an essential part in a quantum key distribution (QKD) system, distilling a highly secure key from a partially secure string by public negotiation between two parties. The optimization objectives of privacy amplification for QKD are large block size, high throughput and low cost. For the global optimization of these objectives, a novel privacy amplification algorithm is proposed in this paper by combining multilinear-modular-hashing and modular arithmetic hashing. This paper proves the security of this hybrid hashing PA algorithm within the framework of both inform…

A simpler proof of zero-knowledge against quantum attacks using Grover's amplitude amplification

Watrous had presented the first proof of zero-knowledge property of a proof system against a quantum verifier. The key of the proof is the construction of a quantum simulator. In the construction, the 'failure state' is rotated to the 'success' state by a tricky operation which is initially developped for the amplification of QMA proof systems. This manuscript presents a new and simpler construction of a simulator. In the construction, we simply amplify the success probability of a classical simulator using Grover's amplification.

Measurement-Based Noiseless Linear Amplification for Quantum Communication

Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We measure an effective entangled r…

Improved Polar-code-based Efficient Post-processing Algorithm for Quantum Key Distribution

Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and …

Quantum feedback amplification

Quantum amplification is essential for various quantum technologies such as communication and weak-signal detection. However, its practical use is still limited due to inevitable device fragility that brings about distortion in the output signal or state. This paper presents a general theory that solves this critical issue. The key idea is simple and easy to implement: just a passive feedback of the amplifier's auxiliary mode, which is usually thrown away. In fact, this scheme makes the controlled amplifier significantly robust, and furthermore it realizes the minimum-noise amplification even …

Heralded photon amplification for quantum communication

Heralded noiseless amplification based on single-photon sources and linear optics is ideally suited for long-distance quantum communication tasks based on discrete variables. We experimentally demonstrate such an amplifier, operating at telecommunication wavelengths. Coherent amplification is performed with a gain of G=1.98+/-0.2, for a state with a maximum expected gain G=2. We also demonstrate that there is no need for a stable phase reference between the initial signal state and the local auxiliary photons used by the amplifier. These results highlight the potential of heralded quantum ampl…

Distillation of Gaussian Einstein-Podolsky-Rosen steering with noiseless linear amplification

Einstein-Podolsky-Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. For practical applications, it remains a challenge to protect EPR steering from decoherence due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environments using measurement-based noiseless linear amplification. Different from entanglement distillation, the extension of steerable region happens in the distillation of EPR steering be…

Heralded amplification of nonlocality via entanglement swapping for long-distance device-independent quantum key distribution

To realize the practical implementation of device-independent quantum key distribution~(DIQKD), the main difficulty is that its security relies on the detection-loophole-free violation of the Clauser-Horne-Shimony-Holt~(CHSH) inequality, i.e. the CHSH value $S>2$, which is easily destroyed by the loss in transmission channels. One of the simplest methods to circumvent it is to utilize the entanglement swapping relay~(ESR). Here, we propose and experimentally test an improved version of the heralded nonlocality amplifier protocol based on the ESR, and numerically show that our scheme is much mo…

Heralded Amplification of Path Entangled Quantum States

Device-independent quantum key distribution (DI-QKD) represents one of the most fascinating challenges in quantum communication, exploiting concepts of fundamental physics, namely Bell tests of nonlocality, to ensure the security of a communication link. This requires the loophole-free violation of a Bell inequality, which is intrinsically difficult due to losses in fibre optic transmission channels. Heralded photon amplification is a teleportation-based protocol that has been proposed as a means to overcome transmission loss for DI-QKD. Here we demonstrate heralded photon amplification for pa…

非信号隐私放大的不可能性

The impossibility of non-signaling privacy amplification

本文指出Barrett等人提出的基于非信号假设的量子密钥协议存在容错和效率缺陷，并证明针对最重要的非局域行为及任意哈希函数，非信号保密性的隐私放大是不可能的。

Fully passive entanglement based quantum key distribution scheme

In general, generation of entangled photon pairs and also the random choice of measurement basis can be implemented with passive optical devices in entanglement based quantum key distribution (QKD) system. However, auxiliary random numbers are still mandatory for conducting the privacy amplification procedure. In this paper, we propose a fully passive entanglement based QKD scheme in which certified random bits for privacy amplification are extracted from detection events of measurement-basis-mismatched entangled photon pairs. The privacy of these random bits can be certified by estimating the…

Quantum Dynamics of Non-Degenerate Parametric Amplification

A simple model of a two-mode non-resonant parametric amplifier is studied with special regard to non-classical features such as revivals and squeezing. The methods used apply for an arbitrary pump parameter. Detailed analytical and explicit expressions are given when the coupling of the two modes has an harmonic time-dependence. Despite its simplicity the model exhibits a very broad range of intricate physical effects. We show that quantum revivals are possible for a broad continuous range of physical parameters in the case of initial Fock states. For coherent states we find that such revivals…

Heralded amplification of photonic qubits

We demonstrate heralded qubit amplification for Time-Bin and Fock-state qubits in an all-fibre, telecom-wavelength, scheme that highlights the simplicity, the stability and potential for fully integrated photonic solutions. Exploiting high-efficiency superconducting detectors, the gain, the fidelity and the performance of the amplifier are studied as a function of loss. We also demonstrate the first heralded Fock-state qubit amplifier without post-selection. This provides a significant advance towards demonstrating Device-Independent Quantum Key Distribution as well as fundamental tests of qua…

克尔非线性谐振器中的参量放大：约瑟夫森参量放大器的理论综述

Parametric Amplification in Kerr Nonlinear Resonators: A theoretical review of Josephson Parametric Amplifiers

本文对超导电路中用于量子极限信号放大的约瑟夫森参量放大器（JPAs）开展理论综述，推导强泵浦下的动力学方程与稳态解，线性化分析弱信号响应并得到增益表达式，数值探究增益与频率失谐、泵浦强度的关系，为该领域后续研究提供参考。

Amplification, Redundancy, and the Quantum Chernoff Information

Amplification was regarded, since the early days of quantum theory, as a mysterious ingredient that endows quantum microstates with macroscopic consequences, key to the "collapse of the wavepacket", and a way to avoid embarrassing problems exemplified by Schrödinger's cat. Such a bridge between the quantum microworld and the classical world of our experience was postulated ad hoc in the Copenhagen Interpretation. Quantum Darwinism views amplification as replication, in many copies, of the information about quantum states. We show that such amplification is a natural consequence of a broad clas…

一种基于编码序列隐私放大机制的无量子记忆量子安全直传协议

A Quantum-Memory-Free Quantum Secure Direct Communication Protocol Based on Privacy Amplification of Coded Sequences

本文提出一种无需传统量子密钥分发协议和一次性垫的量子安全直传协议，通过编码序列的隐私放大理论提升安全性。

Two-sided Quantum Amplitude Amplification and Exact-Error Algorithms

Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search algorithms where input is accessed in the form of black-box queries. We generalize amplitude amplification for two-sided error quantum algorithm for decision problems in the familiar form where input is accessed in the form of initial states of quantum circuits and where arbitrary projective measurements may be used to ascertain success or failure. This genera…

Secure continuous variable quantum teleportation and Einstein-Podolsky-Rosen steering

We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum tele-amplification protocols, that allow non-unity classical gains and a pre-amplification or post-attenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes sugge…

采用相位不敏感和相位敏感放大器的多跨段链路连续变量量子密钥分发

Continuous-variable quantum key distribution over multispan links employing phase-insensitive and phase-sensitive amplifiers

本研究针对光纤传输损耗阻碍长距离量子密钥分发的问题，提出在多跨段链路中使用相位不敏感或相位敏感放大器，并在不同安全框架下分析密钥生成率，证明光放大能提升性能。

超越最坏情况分支：通过振幅放大的量子树搜索

Beyond Worst-Case Branching: Quantum Tree Search via Amplitude Amplification

本文利用振幅放大实现量子树搜索，将查询复杂度从基于最大分支因子的$\sqrt{(b_{max})^m}$改进为基于平均分支因子的$\sqrt{(b_{avg})^m}$，并引入基于采样的树结构估计和量子贪心搜索。

单次量子态分类中的非线性量子放大

Single-shot Quantum State Classification via Nonlinear Quantum Amplification

本文提出通过非线性量子放大实现单次量子态分类，优化测量链以提升分类性能，揭示非线性放大在量子态鉴别中的优势与局限。

Quantum functionalities via feedback amplification

Feedback amplification is a key technique for synthesizing various important functionalities, especially in electronic circuits involving op-amps. This paper presents a quantum version of this methodology, where the general phase-preserving quantum amplifier and coherent (i.e., measurement-free) feedback are employed to construct various type of systems having useful functionalities: quantum versions of differentiator, integrator, self-oscillator, and active filters. The class of active filters includes the Butterworth filter, which can be used to enhance the capacity of an optical quantum com…

协同自旋放大

Cooperative Spin Amplification

本文提出利用反馈回路中协同129Xe核自旋实现信号放大，将磁场预增强超三个数量级，实现4.0 fT/Hz^{1/2}超高磁灵敏度，超越光子散粒噪声和自旋投影噪声，可用于暗物质搜寻等应用。

一个好密钥，L个密钥更好：列表解码与量子隐私放大

One Key Good, L Keys Better: List Decoding Meets Quantum Privacy Amplification

本文提出列表隐私放大(LPA)，在量子密钥分发中通过列表提取提升密钥长度，证明量子列表剩余哈希引理，展示其在BB84型QKD中的应用及优势。

渐近与催化变换中量子相干的任意放大

Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation

本文证明在渐近与催化变换两种操作设定下，任意低相干态均可任意好地转换为任意高相干态，且催化剂可将相干蒸馏速率从零提升至无限，揭示了相干资源理论区别于纠缠与量子热力学的独特性质。