Implementable Quantum Bit-String Commitment Protocol

Quantum bit-string commitment[A.Kent, Phys.Rev.Lett., 90, 237901 (2003)] or QBSC is a variant of bit commitment (BC). In this paper, we propose a new QBSC protocol that can be implemented using currently available technology, and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.Comment: To appear in Phys. Rev. A., 9 pages, 2 figure

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet

The spin-lattice relaxation rate $T_{1}^{-1}$ and NMR spectra of $^1$H in single crystal molecular magnets of Fe8 have been measured down to 15 mK. The relaxation rate $T_1^{-1}$ shows a strong temperature dependence down to 400 mK. The relaxation is well explained in terms of the thermal transition of the iron state between the discreet energy levels of the total spin S=10. The relaxation time $T_1$ becomes temperature independent below 300 mK and is longer than 100 s. In this temperature region stepwise recovery of the $^1$H-NMR signal after saturation was observed depending on the return field of the sweep field. This phenomenon is attributed to resonant quantum tunneling at the fields where levels cross and is discussed in terms of the Landau-Zener transition.Comment: 13 pages, 5 figure

Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion

We provide exact analytical expressions for the magnetic susceptibility function in the high temperature expansion for finite Heisenberg spin systems with an arbitrary coupling matrix, arbitrary single-spin quantum number, and arbitrary number of spins. The results can be used to determine unknown exchange parameters from zero-field magnetic susceptibility measurements without diagonalizing the system Hamiltonian. We demonstrate the possibility of reconstructing the exchange parameters from simulated data for two specific model systems. We examine the accuracy and stability of the proposed method.Comment: 13 pages, 7 figures, submitted to Phys. Rev.

Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for the high nuclearity spin clusters, Mn_{12}, Fe_8 and V_{15}. The largest calculation involves the Mn_{12} cluster which spans a Fock space of a hundred million. Our results show that the earlier estimates of the exchange constants need to be revised for the Mn_{12} cluster to explain the level ordering of low-lying eigenstates. In the case of the Fe_8 cluster, correct level ordering can be obtained which is consistent with the exchange constants for the already known clusters with butterfly structure. In the V_{15} cluster, we obtain an effective Hamiltonian that reproduces exactly, the eight low-lying eigenvalues of the full Hamiltonian.Comment: Revtex, 12 pages, 16 eps figures; this is the final published versio

CSIDH on the surface

For primes p≡3mod4, we show that setting up CSIDH on the surface, i.e., using supersingular elliptic curves with endomorphism ring Z[(1+−p−−−√)/2], amounts to just a few sign switches in the underlying arithmetic. If p≡7mod8 then horizontal 2-isogenies can be used to help compute the class group action. The formulas we derive for these 2-isogenies are very efficient (they basically amount to a single exponentiation in Fp) and allow for a noticeable speed-up, e.g., our resulting CSURF-512 protocol runs about 5.68% faster than CSIDH-512. This improvement is completely orthogonal to all previous speed-ups, constant-time measures and construction of cryptographic primitives that have appeared in the literature so far. At the same time, moving to the surface gets rid of the redundant factor Z3 of the acting ideal-class group, which is present in the case of CSIDH and offers no extra security

High frequency resonant experiments in Fe8_8 molecular clusters

Precise resonant experiments on Fe$_{8}$ magnetic clusters have been conducted down to 1.2 K at various tranverse magnetic fields, using a cylindrical resonator cavity with 40 different frequencies between 37 GHz and 110 GHz. All the observed resonances for both single crystal and oriented powder, have been fitted by the eigenstates of the hamiltonian ${\cal H}=-DS_z^2+ES_x^2-g\mu_B{\bf H}\cdot {\bf S}$. We have identified the resonances corresponding to the coherent quantum oscillations for different orientations of spin S = 10.Comment: to appear in Phys.Rev. B (August 2000

Characterization of the S = 9 excited state in Fe8Br8 by Electron Paramagnetic Resonance

High Frequency electron paramagnetic resonance has been used to observe the magnetic dipole, $\Delta$ M$_s$ = $\pm$ 1, transitions in the $S = 9$ excited state of the single molecule magnet Fe$_8$Br$_8$. A Boltzmann analysis of the measured intensities locates it at 24 $\pm$ 2 K above the $S = 10$ ground state, while the line positions yield its magnetic parameters D = -0.27 K, E = $\pm$0.05 K, and B$_4^0$ = -1.3$\times$ 10$^{-6}$ K. D is thus smaller by 8% and E larger by 7% than for $S = 10$. The anisotropy barrier for $S = 9$ is estimated as 22 K,which is 25% smaller than that for $S = 10$ (29 K). These data also help assign the spin exchange constants(J's) and thus provide a basis for improved electronic structure calculations of Fe$_8$Br$_8$.Comment: 7 pages, Figs included in text, submitted to PR

Magnetic Anisotropy in the Molecular Complex V15

We apply degenerate perturbation theory to investigate the effects of magnetic anisotropy in the magnetic molecule V15. Magnetic anisotropy is introduced via Dzyaloshinskii-Moriya (DM) interaction in the full Hilbert space of the system. Our model provides an explanation for the rounding of transitions in the magnetization as a function of applied field at low temperature, from which an estimate for the DM interaction is found. We find that the calculated energy differences of the lowest energy states are consistent with the available data. Our model also offers a novel explanation for the hysteretic nature of the time-dependent magnetization data.Comment: Final versio

Improved Classical Cryptanalysis of SIKE in Practice

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Nuclear spin-lattice relaxation in ferrimagnetic clusters and chains: A contrast between zero and one dimensions

Motivated by ferrimagnetic oligonuclear and chain compounds synthesized by Caneschi et al., both of which consist of alternating manganese(II) ions and nitronyl-nitroxide radicals, we calculate the nuclear spin-lattice relaxation rate 1/T_1 employing a recently developed modified spin-wave theory. 1/T_1 as a function of temperature drastically varies with the location of probe nuclei in both clusters and chains, though the relaxation time scale is much larger in zero dimension than in one dimension. 1/T_1 as a function of an applied field in long chains forms a striking contrast to that in finite clusters, diverging with decreasing field like inverse square root at low temperatures and logarithmically at high temperatures.Comment: to be published in Phys. Rev. B 68 August 01 (2003