arXiv subjects

H. F. Chau

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

At least 55 records · Page 3Linked to original sources

arXiv2012

Induced Metric And Matrix Inequalities On Unitary Matrices

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] showed that one can define certain metrics and pseudo-metrics on U(n), the group of all $n\times n$ unitary matrices, based on the arguments of the eigenvalues of the unitary matrices. More importantly, these metrics and pseudo-metrics have quantum information theoretical meanings. So it is instructive to study this kind of metrics and pseudo-metrics on U(n). Here we show that any symmetric norm on ${\mathbb R}^n$ induces a metric on U(n). Furthermore, using the same technique, we prove an inequality concerning the eigenvalues of a product of two unitary matrices which generalizes a few inequalities obtained earlier by Chau [arXiv:1006.3614v1].

math-ph↗

arXiv2011

Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices

By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found. Interestingly, this family of metrics can be naturally converted into useful indicators of the degree of non-commutativity between two unitary matrices.

quant-ph↗

arXiv2011

Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.

quant-ph↗

arXiv2010

Comment on "Connection between entanglement and the speed of quantum evolution"

Batle et al. [Phys. Rev. A {\bf 72}, 032337 (2005)] and Borrás et al. [Phys. Rev. A {\bf 74}, 022326 (2006)] studied the connection between entanglement and speed of quantum evolution for certain low-dimensional bipartite quantum states. However, their studies did not cover all possible cases. And the relation between entanglement and the maximum possible quantum evolution speed for these uncovered cases can very different from the ones that they have studied.

quant-ph↗

arXiv2010

Universal Squash Model For Optical Communications Using Linear Optics And Threshold Detectors

The transmission of photons through open-air or an optical fiber is an important primitive in quantum information processing. Theoretical description of such a transmission process often considers only a single photon as the information carrier and thus fails to accurately describe experimental optical implementations where any number of photons may enter a detector. It is important to bridge this big gap between experimental implementations and the theoretical description. One powerful method that emerges from recent efforts to achieve this goal is to consider a squash model that conceptually converts multi-photon states to single-photon states, thereby justifying the equivalence between theory and experiments. However, up to now, only a limited number of protocols admit a squash model; furthermore, a no-go theorem has been proven which appears to rule out the existence of a universal squash model. Here, we observe that an apparently necessary condition demanded by all existing squash models to preserve measurement statistics is too stringent a requirement for many protocols. By chopping this requirement, we show that rather surprisingly, a universal squash model actually exists for a wide range of protocols including quantum key distribution protocols, quantum state tomography, the testing of Bell's inequalities, and entanglement verification, despite the standard no-go theorem.

quant-ph↗

arXiv2010

Practical Entanglement Distillation Scheme Using Recurrence Method And Quantum Low Density Parity Check Codes

Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice. In this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code is found to give the highest yield for Werner states over a wide range of noise level --- the yield for using this QLDPC code is higher than the first runner up by more than 25\% over a wide parameter range. In this respect, the effectiveness of using QLDPC codes in practical entanglement distillation is illustrated.

quant-ph↗

arXiv2010

Tight Upper Bound Of The Maximum Speed Of Evolution Of A Quantum State

I report a tight upper bound of the maximum speed of evolution from one quantum state $ρ$ to another $ρ'$ with fidelity $F(ρ,ρ')$ less than or equal to an arbitrary but fixed value under the action of a time-independent Hamiltonian. Since the bound is directly proportional to the average absolute deviation from the median of the energy of the state ${\mathscr D}E$, one may interpret ${\mathscr D}E$ as a meaningful measure of the maximum information processing capability of a system.

quant-ph↗

arXiv2009

Practical issues in quantum-key-distribution post-processing

Quantum key distribution (QKD) is a secure key generation method between two distant parties by wisely exploiting properties of quantum mechanics. In QKD, experimental measurement outcomes on quantum states are transformed by the two parties to a secret key. This transformation is composed of many logical steps (as guided by security proofs), which together will ultimately determine the length of the final secret key and its security. We detail the procedure for performing such classical post-processing taking into account practical concerns (including the finite-size effect and authentication and encryption for classical communications). This procedure is directly applicable to realistic QKD experiments, and thus serves as a recipe that specifies what post-processing operations are needed and what the security level is for certain lengths of the keys. Our result is applicable to the BB84 protocol with a single or entangled photon source.

quant-ph↗

arXiv2009

On The Critical Packet Injection Rate Of A Preferential Next-Nearest Neighbor Routing Traffic Model On Barabasi-Albert Networks

Recently, Yin et al. [Eur. Phys. J. B 49, 205 (2006)] introduced an efficient small-world network traffic model using preferential next-nearest neighbor routing strategy with the so-called path iteration avoidance (PIA) rule to study the jamming transition of internet. Here we study their model without PIA rule by a mean-field analysis which carefully divides the message packets into two types. Then, we argue that our mean-field analysis is also applicable in the presence of PIA rule in the limit of a large number of nodes in the network. Our analysis gives an explicit expression of the critical packet injection rate $R_c$ as a function of a bias parameter of the routing strategy $α$ in their model with or without PIA rule. In particular, we predict a sudden change in $R_c$ at a certain value of $α$. These predictions agree quite well with our extensive computer simulations.

physics.soc-ph↗

arXiv2009

Practical post-processing for quantum-key-distribution experiments

Quantum key distribution (QKD) promises unconditionally secure key generation between two distant parties by wisely exploiting properties of quantum mechanics. In QKD, experimental measurements on quantum states are transformed to a secret key and this has to be done in accordance with a security proof. Unfortunately, many theoretical proofs are not readily implementable in experiments and do not consider all practical issues. Therefore, in order to bridge this "practical gap", we integrate a few existing theoretical results together with new developments, in effect producing a simple and complete recipe for classical post-processing that one can follow to derive a secret key from the measurement outcomes in an actual QKD experiment. This integration is non-trivial and our consideration is both practical and comprehensive in the sense that we take into account the finiteness of the key length and consider the effects on security of several essential primitives (including authentication, error handling, and privacy amplification). Furthermore, we quantify the security of the final secret key that is universally composable. We show that the finite-size effect mainly comes from phase error estimation. Our result is applicable to the BB84 protocol with a single or entangled photon source.

quant-ph↗

arXiv2008

Getting Information on Independently Prepared Quantum States -- When Are Individual Measurements as Powerful as Joint Measurements?

Given a composite quantum system in which the states of the subsystems are independently (but not necessarily identically) prepared, we construct separate measurements on the subsystems from any given joint measurement such that the former always give at least as large information as the latter. This construction offers new insights into the understanding of measurements on this type of composite systems. Moreover, this construction essentially proves the intuition that separate measurements on the subsystems are sufficient to extract the maximal information about the separately prepared subsystems, thus making a joint measurement unnecessary. Furthermore, our result implies that individual attacks are as powerful as collective attacks in obtaining information on the raw key in quantum key distribution.

quant-ph↗

arXiv2008

Purifying GHZ States Using Degenerate Quantum Codes

Degenerate quantum codes are codes that do not reveal the complete error syndrome. Their ability to conceal the complete error syndrome makes them powerful resources in certain quantum information processing tasks. In particular, the most error-tolerant way to purify depolarized Bell states using one-way communication known to date involves degenerate quantum codes. Here we study three closely related purification schemes for depolarized GHZ states shared among $m \geq 3$ players by means of degenerate quantum codes and one-way classical communications. We find that our schemes tolerate more noise than all other one-way schemes known to date, further demonstrating the effectiveness of degenerate quantum codes in quantum information processing.

quant-ph↗

arXiv2008

An Adaptive Entanglement Distillation Scheme Using Quantum Low Density Parity Check Codes

Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical performance analysis of an adaptive entanglement distillation scheme using QLDPC codes. In particular, we find that the expected yield of our adaptive distillation scheme to combat depolarization errors exceed that of Leung and Shor whenever the error probability is less than about 0.07 or greater than about 0.28. This finding illustrates the effectiveness of using QLDPC codes in entanglement distillation.

quant-ph↗

arXiv2008

Playing The Hypothesis Testing Minority Game In The Maximal Reduced Strategy Space

Hypothesis Testing Minority Game (HMG) is a variant of the standard Minority Game (MG) that models the inertial behavior of agents in the market. In the earlier study of our group, we find that agents cooperate better in HMG than in the standard MG when strategies are picked from the full strategy space. Here we continue to study the behavior of HMG when strategies are chosen from the maximal reduced strategy space. Surprisingly, we find that, unlike the standard MG, the level of cooperation in HMG depends strongly on the strategy space used. In addition, a novel intermittency dynamics is also observed in the minority choice time series in a certain parameter range in which the orderly phases are characterized by a variety of periodic dynamics. Remarkably, all these findings can be explained by the crowd-anticrowd theory.

physics.soc-ph↗

arXiv2007

Reply To "Comment on 'Quantum String Seal Is Insecure' "

In Phys. Rev. A. 76, 056301 (2007), He claimed that the proof in my earlier paper [Phys. Rev. A 75, 012327 (2007)] is insufficient to conclude the insecurity of all quantum string seals because my measurement strategy cannot obtain non-trivial information on the sealed string and escape detection at the same time. Here, I clarify that our disagreement comes from our adoption of two different criteria on the minimum amount of information a quantum string seal can reveal to members of the public. I also point out that He did not follow my measurement strategy correctly.

quant-ph↗

arXiv2006

Weighted Assortative And Disassortative Networks Model

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by topological growth as well as by weight change. In addition, we introduce the weighted assortativity coefficient, which generalizes the assortativity coefficient of a topological network, to measure the tendency of having a high-weighted link between two vertices of similar degrees. Network generated by our model exhibits scale-free behavior with a tunable exponent. Besides, a few non-trivial features found in real-world networks are reproduced by varying the parameter ruling the speed of weight evolution. Most importantly, by studying the weighted assortativity coefficient, we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative.

physics.soc-ph↗

arXiv2006

Quantum String Seal Is Insecure

A quantum string seal encodes the value of a (bit) string as a quantum state in such a way that everyone can extract a non-negligible amount of available information on the string by a suitable measurement. Moreover, such measurement must disturb the quantum state and is likely to be detected by an authorized verifier. In this way, the intactness of the encoded quantum state plays the role of a wax seal in the digital world. Here I analyze the security of quantum string seal by studying the information disturbance tradeoff of a measurement. This information disturbance tradeoff analysis extends the earlier results of Bechmann-Pasquinucci et al. and Chau by concluding that all quantum string seals are insecure. Specifically, I find a way to obtain non-trivial available information on the string that escapes the verifier's detection with at least 50% chance.

quant-ph↗

arXiv2006

Insecurity Of Imperfect Quantum Bit Seal

Quantum bit seal is a way to encode a classical bit quantum mechanically so that everyone can obtain non-zero information on the value of the bit. Moreover, such an attempt should have a high chance of being detected by an authorized verifier. Surely, a reader looks for a way to get the maximum amount of information on the sealed bit and at the same time to minimize her chance of being caught. And a verifier picks a sealing scheme that maximizes his chance of detecting any measurement of the sealed bit. Here, I report a strategy that passes all measurement detection procedures at least half of the time for all quantum bit sealing schemes. This strategy also minimizes a reader's chance of being caught under a certain scheme. In this way, I extend the result of Bechmann-Pasquinucci et al. by proving that quantum seal is insecure in the case of imperfect sealed bit recovery.

quant-ph↗