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H. F. Chau

Publications and source records attributed to H. F. Chau.

At least 19 recordsLinked to original sources
arXiv2026

From Certifying Rank $k$ Projectors To Non-Positivity, Entanglement, And Non-Hermitian Witnesses Through Traces Of Matrix Powers

We all know that a density matrix $ρ$ is pure if and only if $\mathrm{Tr} \,ρ^2 = 1$. But is this the only way to prove the purity of $ρ$ using the trace of its powers? Here I systematically study the necessary and sufficient conditions of the more general question of guaranteeing that all eigenvalues of a Hermitian matrix belong to a specified set through its trace of powers. More importantly, these characterization results are automatically witnesses certifying a quantum state as entangled, a Hermitian operator has least one negative eigenvalue and a linear operator as non-Hermitian. I demonstrate the effectiveness of these witnesses, analyze their performance, and study their strength, weakness together with resource requirement through numerical simulation as well as analytical work. I also discuss briefly the effects of numerical stability, uncertainty in measurement and rounding errors on these problems.

quant-ph↗
arXiv2026

Fully Passive Quantum Conference Key Agreement

Quantum Conference Key Agreement (CKA) provides a secure method for multi-party communication. A recently developed interference-based prepare-and-measure quantum CKA possesses the advantages of measurement-device-independence, namely, being immune to side-channels from the detector side. Besides, it achieves good key rate performance, especially for high-loss channels, due to the use of single photon interference. Meanwhile, several fully passive QKD schemes have been proposed, which eliminate all side channels from the source modulation side. We extend the fully passive idea to an interference-based CKA, which has a high level of implementation security for many-user communication.

quant-ph↗
arXiv2026

Quantum Speed Limits For Open System Dynamics Based On A Representation-Basis-Dependent $\boldsymbol{\ell^{p}_{w}}$-Seminorm

We report a family of quantum speed limits (QSLs) that give evolution time lower bounds between an initial and a final state whose separation is described by a certain representation basis dependent norm derived from the weighted $\ell^{p}_{w}$-seminorm. These QSLs are applicable to open, closed, time-dependent, or time-independent systems in finite-dimensional Hilbert spaces whose density matrices are piecewise time differentiable. They can be extended to systems over separable Hilbert spaces as well. Crucially, these QSLs are valid for arbitrary operators, not just density matrices, provided that a modest technical condition is fulfilled. When compared to the existing QSLs applied to pure state time-independent Hamiltonian evolution, qubit spontaneous emission, high-fidelity gate implementation, coherent state photon loss and operator coherence or dephasing, ours consistently show improved sharpness in most cases, along with greater universality and still retaining computational efficiency.

quant-ph↗
arXiv2026

Fully-Passive Twin-Field Quantum Key Distribution

We propose a fully passive twin-field quantum key distribution (QKD) setup where basis choice, decoy-state preparation and encoding are all implemented entirely by post-processing without any active modulation. Our protocol can remove the potential side-channels from both source modulators and detectors, and additionally retain the high key rate advantage offered by twin-field QKD, thus offering great implementation security and good performance. Importantly, we also propose a post-processing strategy that uses mismatched phase slices and minimizes the effect of sifting. We show with numerical simulation that the new protocol can still beat the repeaterless bound and provide satisfactory key rate.

quant-ph↗
arXiv2026

Modified Axelrod Model Showing Opinion Convergence And Polarization In Realistic Scale-Free Networks

Axelrod model is an opinion dynamics model such that each agent on a square lattice has a finite number of possible nominal opinions on a finite number of issues that are usually called features in the field. Moreover, its dynamics between two agents is assimilative in the sense that the number of agreeing features between them never decreases upon interaction. Here we modify this model to study opinion convergence, polarization and more importantly to find ways to reduce opinion polarization in an already polarized population. We do so by changing or adding several elements from complex network and continuous opinion dynamics research. First, we put agents in a scale-free network. Second, we adopt the bounded confidence model by representing our agent's opinions by numbers in $[-1,1]$ those distances follow the standard Euclidean metric. Third, our rules allow both convergence and divergence of their resultant opinions after a pair of agents interacts. As a result, our modified model offers a more comprehensive exploration of opinion dynamics. Computer simulation results of our model show scaling behavior and a notable trend in opinion polarization on all features in the majority of reasonable simulation parameters. To mitigate this polarization, we introduce empathetic agents that work actively to reduce opinion differences. However, our findings indicate limited success in the approach for the most effective way is to change the behavior of a significant portion of highly connected agents. This research contributes to the understanding of opinion dynamics within society and highlights the nuanced complexities that arise when considering factors such as network structure and continuous opinion values. Our results prompt further exploration and open avenues for future investigations into effective methods of reducing opinion polarization.

physics.soc-ph↗
arXiv2025

One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum cryptography as they can be used to bound the information obtained by an adversary. However, calculating the exact value or non-trivial bounds of min-entropy are extremely difficult because the composite system dimension may scale exponentially with the dimension of its subsystem. Here, we develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state that is applicable to both finite and infinite dimensional reduced quantum states. Moreover, we show our technique is of practical interest in at least three situations. First, it offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme. Second, it gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol. Third, it provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol. These results show the effectiveness and wide applicability of our approach.

quant-ph↗
arXiv2024

Efficient Fault-Tolerant Single Qubit Gate Approximation And Universal Quantum Computation Without Using The Solovay-Kitaev Theorem

Arbitrarily accurate fault-tolerant (FT) universal quantum computation can be carried out using the Clifford gates Z, S, CNOT plus the non-Clifford T gate. Moreover, a recent improvement of the Solovay-Kitaev theorem by Kuperberg implies that to approximate any single-qubit gate to an accuracy of $ε> 0$ requires $\text{O}(\log^c[1/ε])$ quantum gates with $c > 1.44042$. Can one do better? That was the question asked by Nielsen and Chuang in their quantum computation textbook. Specifically, they posted a challenge to efficiently approximate single-qubit gate, fault-tolerantly or otherwise, using $Ω(\log[1/ε])$ gates chosen from a finite set. Here I give a partial answer to this question by showing that this is possible using $\text{O}(\log[1/ε] \log\log[1/ε] \log\log\log[1/ε] \cdots)$ FT gates chosen from a finite set depending on the value of $ε$. The key idea is to construct an approximation of any phase gate in a FT way by recursion to any given accuracy $ε> 0$. This method is straightforward to implement, easy to understand, and interestingly does not involve the Solovay-Kitaev theorem.

quant-ph↗
arXiv2024

A Unifying Quantum Speed Limit For Time-Independent Hamiltonian Evolution

Quantum speed limit (QSL) is the study of fundamental limits on the evolution time of quantum systems. For instance, under the action of a time-independent Hamiltonian, the evolution time between an initial and a final quantum state obeys various mutually complementary lower bounds. They include the Mandelstam-Tamm, Margolus-Levitin, Luo-Zhang, dual ML and Lee-Chau bounds. Here we show that the Mandelstam-Tamm bound can be obtained by optimizing the Lee-Chau bound over a certain parameter. More importantly, we report a QSL that includes all the above bounds as special cases before optimizing over the physically meaningless reference energy level of a quantum system. This unifying bound depends on a certain parameter $p$. For any fixed $p$, we find all pairs of time-independent Hamiltonian and initial pure quantum state that saturate this unifying bound. More importantly, these pairs allow us to compute this bound accurately and efficiently using an oracle that returns certain $p$th moments related to the absolute value of energy of the quantum state. Moreover, this oracle can be simulated by a computationally efficient and accurate algorithm for finite-dimensional quantum systems as well as for certain infinite-dimensional quantum states with bounded and continuous energy spectra. This makes our computational method feasible in a lot of practical situations. We compare the performance of this bound for the case of a fixed $p$ as well as the case of optimizing over $p$ with existing QSLs. We find that if the dimension of the underlying Hilbert space is $\lesssim 2000$, our unifying bound optimized over $p$ can be computed accurately in a few minutes using Mathematica code with just-in-time compilation in a typical desktop. Besides, this optimized unifying QSL is at least as good as all the existing ones combined and can occasionally be a few percent to a few times better.

quant-ph↗
arXiv2023

$\boldsymbol{α_{>}(ε) = α_{<}(ε)}$ For The Margolus-Levitin Quantum Speed Limit Bound

The Margolus-Levitin (ML) bound says that for any time-independent Hamiltonian, the time needed to evolve from one quantum state to another is at least $πα(ε) / (2 \langle E-E_0 \rangle)$, where $\langle E-E_0 \rangle$ is the expected energy of the system relative to the ground state of the Hamiltonian and $α(ε)$ is a function of the fidelity $ε$ between the two state. For a long time, only a upper bound $α_{>}(ε)$ and lower bound $α_{<}(ε)$ are known although they agree up to at least seven significant figures. Lately, Hörnedal and Sönnerborn proved an analytical expression for $α(ε)$, fully classified systems whose evolution times saturate the ML bound, and gave this bound a symplectic-geometric interpretation. Here I solve the same problem through an elementary proof of the ML bound. By explicitly finding all the states that saturate the ML bound, I show that $α_{>}(ε)$ is indeed equal to $α_{<}(ε)$. More importantly, I point out a numerical stability issue in computing $α_{>}(ε)$ and report a simple way to evaluate it efficiently and accurately.

quant-ph↗
arXiv2023

Reducing The Impact Of Adaptive Optics Lag On Optical And Quantum Communications Rates From Rapidly Moving Sources

Wavefront of light passing through turbulent atmosphere gets distorted. This causes signal loss in free-space optical communication as the light beam spreads and wanders at the receiving end. Frequency and/or time division multiplexing adaptive optics (AO) techniques have been used to conjugate this kind of wavefront distortion. However, if the signal beam moves relative to the atmosphere, the AO system performance degrades due to high temporal anisoplanatism. Here we solve this problem by adding a pioneer beacon that is spatially separated from the signal beam with time delay between spatially separated pulses. More importantly, our protocol works irrespective of the signal beam intensity and hence is also applicable to secret quantum communication. In particular, using semi-empirical atmospheric turbulence calculation, we show that for low earth orbit satellite-to-ground decoy state quantum key distribution with the satellite at zenith angle $< 30^\circ$, our method increases the key rate by at least $215\%$ and $40\%$ for satellite altitude $400$~km and $800$~km, respectively. Finally, we propose a modification of existing wavelength division multiplexing systems as an effective alternative solution to this problem.

quant-ph↗
arXiv2021

Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders

Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here we show that the ability to place N completely depolarising channels in a superposition of N alternative causal orders enables a high-fidelity, heralded transmission of quantum information with error vanishing as 1/N. This phenomenon highlights a fundamental difference with the N = 2 case, where completely depolarising channels are unable to transmit quantum data, even when placed in a superposition of causal orders. The ability to place quantum channels in a superposition of orders also leads to an increase of the classical communication capacity with N, which we rigorously prove by deriving an exact single-letter expression. Our results highlight the more complex patterns of correlations arising from multiple causal orders, which are similar to the more complex patterns of entanglement arising in multipartite quantum systems.

quant-ph↗
arXiv2020

Security Of Finite-Key-Length Measurement-Device-Independent Quantum Key Distribution Using Arbitrary Number Of Decoys

In quantum key distribution, measurement-device-independent and decoy-state techniques enable the two cooperative agents to establish a shared secret key using imperfect measurement devices and weak Poissonian sources, respectively. Investigations so far are not comprehensive as they restrict to less than or equal to four decoy states. Moreover, many of them involves pure numerical studies. Here I report a general security proof that works for any fixed number of decoy states and any fixed raw key length. The two key ideas involved here. The first one is the repeated application of the inversion formula for Vandermonde matrix to obtain various bounds on certain yields and error rates. The second one is the use of a recently proven generalization of the McDiarmid inequality. These techniques rise the best provably secure key rate of the measurement-device-independent version of the BB84 scheme by at least 1.25 times and increase the workable distance between the two cooperative agents from slightly less than 60 km to slightly greater than 130 km in case there are $10^{10}$ photon pulse pair sent without a quantum repeater.

quant-ph↗
arXiv2020

Application of an Improved Version of McDiarmid Inequality in Finite-Key-Length Decoy-State Quantum Key Distribution

In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here we report an improved version of McDiarmid inequality in statistics and show how use it to directly compute a lower bound of $R$ via the so-called centering sequence. A novelty in this work is the optimization of the bound through the freedom of choosing possible centering sequences. The provably secure key rate of realistic 100~km long quantum channel obtained by our method is at least twice that of the state-of-the-art procedure when the raw key length $\ell_\text{raw}$ is $\approx 10^5$ to $10^6$. In fact, our method can improve the key rate significantly over a wide range of raw key length from about $10^5$ to $10^{11}$. More importantly, it is achieved by pure theoretical analysis without altering the experimental setup or the post-processing method. In a boarder context, this work introduces powerful concentration inequality techniques in statistics to tackle physics problem beyond straightforward statistical data analysis especially when the data are correlated so that tools like the central limit theorem are not applicable.

quant-ph↗
arXiv2019

Chau-Wang-Wong17 Scheme Is Experimentally More Feasible Than The Six-State Scheme

Recently, Chau et al. [Phys. Rev. A 95, 022311 (2017)] reported a quantum-key-distribution (QKD) scheme using four-dimensional qudits. Surprisingly, as a function of the bit error rate of the raw key, the secret key rate of this scheme is equal to that of the (qubit-based) six-state scheme under one-way classical communication using ideal apparatus in the limit of arbitrarily long raw key length. Here we explain why this is the case in spite of the fact that these two schemes are not linearly related to each other. More importantly, we find that in terms of the four-dimensional dit error rate of the raw key, the Chau et al.'s scheme can tolerate up to 21.6% using one-way classical communications, which is better than the Sheridan and Scarani's scheme [Phys. Rev. A 82, 030301(R) (2010)]. In addition, we argue the experimental advantages of the Chau et al. implementation over the standard six-state scheme and report a corresponding proof-of-principle experiment using passive basis selection with decoy states. We also compare our experiment with the recent high secret key rate implementation of the Sheridan and Scarani's scheme by Islam et al. [Sci. Adv. \text{3}, e1701491].

quant-ph↗
arXiv2018

Application Of McDiarmid Inequality In Finite-Key-Length Decoy-State Quantum Key Distribution

In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here I show how to directly compute a lower bound of $R$ via McDiarmid inequality in statistics. This method increases the provably secure key rate of realistic quantum channels by at least 30% when the raw key length is $\approx 10^5$ to $10^6$. More importantly, this is achieved by pure theoretical analysis without altering the experimental setup or the post-processing method. In a boarder context, this work introduces powerful concentration inequality techniques in statistics to tackle physics problem beyond straightforward statistical data analysis.

quant-ph↗
arXiv2018

Decoy State Quantum Key Distribution With More Than Three Types Of Photon Intensity Pulses

Decoy state method closes source security loophole in quantum key distribution (QKD) using laser source. In this method, accurate estimates of the detection rates of vacuum and single photon events plus the error rate of single photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 1% relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key rate of the BB84 QKD protocol with unbiased bases selection by at least 20% on average in realistic settings. The major tricks are the use of more than three types of photon intensities plus the fact that estimating bounds of the above detection and error rates is numerically stable although these bounds are related to the inversion of a high condition number matrix.

quant-ph↗
arXiv2017

Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme

In comparison to qubit-based protocols, qudit-based quantum key distribution (QKD) ones gen- erally allow two cooperative parties to share unconditionally secure keys under a higher channel noise. However, it is very hard to prepare and measure the required quantum states in qudit-based protocols in general. One exception is the recently proposed highly error tolerant qudit-based proto- col known as the Chau15 [1]. Remarkably, the state preparation and measurement in this protocol can be done relatively easily since the required states are phase encoded almost like the diagonal basis states of a qubit. Here we report the first proof-of-principle demonstration of the Chau15 protocol. One highlight of our experiment is that its post-processing is based on practical one-way manner, while the original proposal in Ref. [1] relies on complicated two-way post-processing, which is a great challenge in experiment. In addition, by manipulating time-bin qudit and measurement with a variable delay interferometer, our realization is extensible to qudit with high-dimensionality and confirms the experimental feasibility of the Chau15 protocol.

quant-ph↗
arXiv2017

Experimentally Feasible Quantum-Key-Distribution Scheme Using Qubit-Like Qudits And Its Comparison With Existing Qubit- and Qudit-Based Protocols

Recently, Chau introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a $2^n$-dimensional Hilbert space in the form $(|i\rangle\pm|j\rangle)/\sqrt{2}$ with $n\ge 2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n-1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of $n=2$, the secret key rate of this modified protocol using non-degenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

quant-ph↗