A quantum analog of Huffman coding

We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded in constructing a Huffman-coding inspired quantum scheme. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be of polylogarithmic depth by a massively parallel implementation of a quantum gate array. This is to be compared with the O (N^3) computational steps required in the sequential implementation by Cleve and DiVincenzo of the well-known quantum noiseless block coding scheme of Schumacher. We also show that O(N^2(log N)^a) computational steps are needed for the communication of quantum information using another Huffman-coding inspired scheme where the sender must disentangle her encoding device before the receiver can perform any measurements on his signals.Comment: Revised version, 7 pages, two-column, RevTex. Presented at 1998 IEEE International Symposium on Information Theor

A mutant of Neurospora crassa deficient in cytochrome c heme lyase activity cannot import cytochrome c into mitochondria

The nuclear cyt-2-1 mutant of Neurospora crassa is characterized by a gross deficiency of cytochrome c (Bertrand, H., and Collins, R. A. (1978) Mol. Gen. Genet. 166, 1-13). The mutant produces mRNA that can be translated into apocytochrome c in vitro. Apocytochrome c is also synthesized in vivo in cyt-2-1, but it is rapidly degraded and thus does not accumulate in the cytosol. Mitochondria from wild-type cells bind apocytochrome c made in vitro from either wild-type or cyt-2-1 mRNA and convert it to holocytochrome c. This conversion depends on the addition of heme by cytochrome c heme lyase and is coupled to translocation of cytochrome c into the intermembrane space. Mitochondria from the cyt-2-1 strain are deficient in the ability to bind apocytochrome c. They are also completely devoid of cytochrome c heme lyase activity. These defects explain the inability of the cyt-2-1 mutant to convert apocytochrome c to the holo form and to import it into mitochondria

The automorphism group of separable states in quantum information theory

We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by \emph{natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. We apply our results to preservers of the product numerical range.Comment: 15 page

Solar neutrino interactions: Using charged currents at SNO to tell neutral currents at Super-Kamiokande

In the presence of flavor oscillations, muon and tau neutrinos can contribute to the Super-Kamiokande (SK) solar neutrino signal through the neutral current process \nu_{\mu,\tau} e^{-}\to \nu_{\mu,\tau} e^{-}. We show how to separate the \nu_e and \nu_{\mu,\tau} event rates in SK in a model independent way, by using the rate of the charged current process \nu_e d \to p p e^{-} from the Sudbury Neutrino Observatory (SNO) experiment, with an appropriate choice of the SK and SNO energy thresholds. Under the additional hypothesis of no oscillations into sterile states, we also show how to determine the absolute ^{8}B neutrino flux from the same data set, independently of the \nu_e survival probability.Comment: 14 pages (RevTeX), incl. 3 figures (epsf), submitted to Phys. ReV.

Chaotic behaviors of a digital filter with two’s complement arithmetic and arbitrary initial conditions and order

This letter shows some counter-intuitive simulation results that the symbolic sequences and the state variables of a digital filter with two’s complement arithmetic and arbitrary initial conditions and order will be eventually zero when all the filter parameters are even numbers, no matter the system matrix of the filter is stable or not

Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

A Field Test Study on Instrumented Soil Nail Installed in Cut Slope

Soil nailing is a technique routinely used in Hong Kong whereby closely spaced steel bars are installed into a slope so that its stability conditions can be improved. A full-scale field test has been carried out by The Department of Civil Engineering of The University of Hong Kong to study the development of passive load along the full length of soil nails when subjected to induced rise in groundwater table. The cut slope was formed to a very steep angle of 55° and 10 m high in completely decomposed volcanic material. Grouted curtain was also formed behind, at the bottom and on both ends of the slope in order to form an impermeable barrier that would allow groundwater table to increase artificially by injecting water into slotted PVC pipes. Nine number of soil nails (in regular 2 m c/c spacing of 3 rows and 3 columns) of 6 m long high yield steel bar were installed at 15° from horizontal into the formed cut slope. Instrumentation included strain gauges along the nails, inclinometers, piezometers, and settlement prisms. This paper describes the method of construction and the load developed along the soil nails when the groundwater table was raised to the ground surface. It was found that the measured passive load along the soil nail was smaller than the commonly assumed design parameters, an indication that substantial savings can be achieved if mobilization of shearing resistance along the full length of the soil nail was considered in routine design. Finite element analysis has also been carried out to compare the measured load with the simulated load and the stability factor is compared with the factor of safety at each stage of loading

Current Management Strategy of Nasopharyngeal Carcinoma

Nasopharyngeal carcinoma is an unique head and neck cancer. It is common among the southern Chinese and is closely associated with the Epstein Barr virus (EBV). To diagnose the disease in its early stage is infrequent as the symptoms are usually trivial and patients only present in late stages. Testing the blood for elevated EBV DNA has now become a screening test for the high risk group of patients, aiming to diagnose the disease in its early stages. Imaging studies, positron emission tomography scans in addition to clinical examination provide information on the extent of the disease. The confirmation of the disease still depends on endoscopic examination and biopsy. Radiotherapy with or without chemotherapy has been the primary treatment modality. The application of intensity modulated radiotherapy and the use of concomitant chemoradiation have improved the control of nasopharyngeal carcinoma together with the reduction of long term side effects. The early detection of residual or recurrence tumor in the neck or at the primary site has allowed delivery of salvage treatment. The choice of the optimal surgical salvage, either for neck disease or primary tumor depends on the extent of the residual or recurrent disease. The outcome of these patients have improved with the application of the appropriate surgical salvage