Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Bit-Oriented Quantum Public-Key Cryptosystem Based on Bell States

Quantum public key encryption system provides information confidentiality using quantum mechanics. This paper presents a quantum public key cryptosystem (QPKC) based on the Bell states. By Holevo’s theorem, the presented scheme provides the security of the secret key using one-wayness during the QPKC. While the QPKC scheme is information theoretic security under chosen plaintext attack (CPA). Finally some important features of presented QPKC scheme can be compared with other QPKC scheme.     

Effects of Final State Interactions in Pure Annihilation Decay of B+ → D+K0*

The decay of the B ⁺ meson to the D ⁺ and K ⁰* mesons is a pure annihilation decay. For this reason, in the framework of the quantum chromodynamics factorization (QCDF) approach, this decay has a small amplitude and a small branching ratio. In this research we find that, before the D ⁺ and K ⁰* mesons are produced in the final states, pair mesons such as D _s ⁺* and D _s ⁺ρ⁰ are produced. The intermediate-state mesons via the exchange of K ⁰(K ⁰*) and D ⁺(D ⁺*) go to the D ⁺ and K ⁰* final state mesons. However we calculate the B ₊ → D ⁺ K ⁰* decay in two different frameworks. The first framework is the QCDF method and the second one is final state interaction (FSI). The experimental branching ratio of B ₊ → D ₊ K ⁰* decay is less than 3 × 10^–6, and our results obtained by the QCDF method and FSI are (0.35 ± 0.04) × 10^–6 and (2.94 ± 0.10) × 10^–6, respectively.     

Electric quadrupole moments of light nuclei and transition probabilities for them in the multiquantum approximation of the orthogonal scheme

A method for calculating electric quadrupole moments of light nuclei and probabilities of electric quadrupole transitions in them in the multiquantum approximation of the orthogonal scheme is proposed. Specific calculations of these quantities are performed for the ₄ ⁸ Be nucleus with allowance for all U(3(A ? 1)) states characterized by the λ = [44] Young diagram, the quantum numbers K _min and K _min + 2 of the O(3A ? 1)) group, and the number E = K + 2N (N = 0, 1, …, 9) of oscillator quanta. It is shown that an extension of the basis from the E = K _min to the E = K _min + 2 approximation leads to an increase of 15 to 45% in the electric quadrupole moments and to an increase in the transition probabilities B(E2) by a factor of 1.6 to 2.8. The inclusion of E = K + 2N (N = 0, 1, …), states involving multiquantum excitations (ρ excitations) increases additionally the results by 10 to 30%. The results of these calculations are compared with their counterparts obtained in the multiquantum approximation of the unitary scheme.     

Almost One Bit Violation for the Additivity of the Minimum Output Entropy

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_k,t. We also showed that the set K_k,t is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of \({\ell^p}\) norms on the set K_k,t and prove that the maximum is attained on a vector of shape (a, b, . . . , b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show that for any \({\varepsilon > 0}\), it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183, and that for appropriate choice of parameters, the violation can be as large as \({\log 2 -\varepsilon}\). Conversely, our result implies that, with probability one in the limit, one does not obtain a violation of additivity using conjugate random quantum channels and the Bell state, in dimension 182 and less.     

On correlators for high multiplicity events

We present the results of the study of the energy correlators K₂(n) and K₃(n) and their ratio R₃(n) as a function of the hadron multiplicity at the LHC. The PYTHIA generator has been used. PYTHIA predicts that R₃(n) is not dependent on multiplicity. K₂(n), K₃(n), and the R₃(n) ratio can be studied at ATLAS.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

A nonradiative intersystem crossing <Emphasis Type="Italic">S</Emphasis>(ππ*) ↝ <Emphasis Type="Italic">T</Emphasis>(ππ*) transition in dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxin

The probability of the nonradiative S-T intersystem crossing in dibenzo-p-dioxin is theoretically studied using a model for the vibronically induced spin-orbit coupling between electronic states and taking into account all out-of-plane vibrational modes. Several symmetry variants for the lowest S ₁(ππ*) singlet state are considered. In the case of g symmetry of this state, a provision is made for the possibility of its vibronic coupling with the nearest dipole-active singlet ¹ B _2u ππ* state. The rate constants K _ST of the S ₁ ? T(ππ*) transitions to the T ₁(³ B _3g ) state are estimated taking into account several intermediate triplet T _m (ππ*) states of g and u symmetry. For different symmetry types of the S ₁ state, the effect of K _ST on the fluorescence quantum yield ?_fl is discussed. The ¹ B _3g symmetry state is found to be the lowest S ₁ state. It is found that the main contribution to K _ST is made by the S ₁(¹ B _3g ) ? T ₄(³ A _g ) transition.     

An Efficient and Secure Arbitrary <Emphasis Type="Italic">N</Emphasis>-Party Quantum Key Agreement Protocol Using Bell States

Two quantum key agreement protocols using Bell states and Bell measurement were recently proposed by Shukla et al. (Quantum Inf. Process. 13(11), 2391–2405, 2014). However, Zhu et al. pointed out that there are some security flaws and proposed an improved version (Quantum Inf. Process. 14(11), 4245–4254, 2015). In this study, we will show Zhu et al.’s improvement still exists some security problems, and its efficiency is not high enough. For solving these problems, we utilize four Pauli operations {I, Z, X, Y} to encode two bits instead of the original two operations {I, X} to encode one bit, and then propose an efficient and secure arbitrary N-party quantum key agreement protocol. In the protocol, the channel checking with decoy single photons is introduced to avoid the eavesdropper’s flip attack, and a post-measurement mechanism is used to prevent against the collusion attack. The security analysis shows the present protocol can guarantee the correctness, security, privacy and fairness of quantum key agreement.     

Practical Analysis of Continuous-Variable Quantum Key Distribution Using a Nondeterministic Noiseless Linear Amplifier

We study the impact of the imperfections and the finite-size effect on the continuous-variable quantum key distribution (CVQKD) protocol with the nondeterministic noiseless linear amplifier (NLA). The imperfections of the homodyne detector and the imperfect amplification process as well as the finite-size effect on parameter estimation procedure are considered. We can see that despite the imperfections of the homodyne detector, the maximum improved transmission distance can still reach the equivalence of 20log₁₀g dB losses theoretically. Moreover, the analysis shows the imperfect amplification process of the NLA will slightly decrease the performance of the system. And we find the finite-size effect significantly influence the secret key rates of the NLA CVQKD protocol and the performance will approach the ideal asymptotic case with the increase of block size.     

A Rigidity Result for Extensions of Braided Tensor <Emphasis Type="Italic">C</Emphasis>*–Categories Derived from Compact Matrix Quantum Groups

Let G be a classical compact Lie group and G _μ the associated compact matrix quantum group deformed by a positive parameter μ (or \({\mu\in{\mathbb R}\setminus\{0\}}\) in the type A case). It is well known that the category of unitary representations of G _μ is a braided tensor C*–category. We show that any braided tensor *–functor \({\rho: \text{Rep}(G_\mu)\to\mathcal{M}}\) to another braided tensor C*–category with irreducible tensor unit is full if |μ| ≠ 1. In particular, the functor of restriction RepG _μ → Rep(K) to a proper compact quantum subgroup K cannot be made into a braided functor. Our result also shows that the Temperley–Lieb category \({\mathcal{T}_{\pm d}}\) for d > 2 can not be embedded properly into a larger category with the same objects as a braided tensor C*–subcategory.     

Die absolute Intensität der durch Elektronenstoß in einer dicken Cu-Antikathode erzeugtenKα-Strahlung

The numberN _Kα ^dir (produced) ofKα-photons produced by electron-bombardment in a thick target of copper per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energy-region up to the four times theK-ionization energyE _K . The result can be presented in the following empirical form:N _Kα ^dir (produced) = 4π·

     

Retardation of unimolecular reactions in the solid phase

The retardation coefficient, K _R = k _l/k _s, for a homogeneous reaction in the bulk of a crystal was calculated within the framework of the free-volume model of unimolecular reactions in the solid phase in the approximation of an isotropic continuum. The key parameters entering into the working formula, more specifically, the additional activation volume for the solid phase and the compressibility coefficient, were estimated using semiempirical methods. The calculated values of K _R range from several units to several thousand units, an interval that encompasses all the experimental values of this quantity. Low values of K _R are indicative of reactions in the bulk of the crystal lattice. In addition, reactions on defects can occur, being predominant at K _R > 100. In all cases, the calculated values of K _R give an upper estimate of the degree of retardation, above which no experimental values have been obtained.     

Glueballs of the <Emphasis Type="Italic">f</Emphasis><Subscript>0</Subscript> and <Emphasis Type="Italic">f</Emphasis><Subscript>2</Subscript> families,observed in processes with Pseudoscalar mesons

Within the approach based on analyticity and unitarity, the experimental data on the isoscalar S and D waves of the ππ → ππ, K\(\bar K\), ηη, ηη′ processes have been jointly analyzed for studying the status and quantum chromodynamics nature of the f ₀ andf ₂ mesons. Assignment of scalar and tensor mesons to lower nonets is proposed. Two states (f ₀ (1500) and f ₂ (2000)) are interpreted as glueballs.     

Population and current noise in semiconductor laser junctions

The population noise in a semiconductor laser is calculated by means of the quantum mechanical Langevin method. The resulting population noise is given by 〈δ N _c ² 〉=(T _c/2) (rate in+rate out)+K(¯n), whereN _c is the total number of electrons in the conduction band in the active region,T _c is a relaxation time. The first expression is the usual shot noise term. The transition rates are the sum of the rates due to the light field, the pumping and the spontaneous emission. The last termK(¯ n) is caused by the light field fluctuations;¯n is the mean number of photons in the laser mode.K(¯ n) consists of two parts: a) The main part is proportional to the intensity noise of the light field, which increases below but near threshold and gets constant above threshold. b) There is a second term due to the fact that parts of the fluctuations of the population and of the light field are correlated. — The noise spectrumS _I(ω) of the junction currentI is calculated for low frequencies. Beyond the usual shot noise termS _I(0)=2eI, additional noise is found in and above the threshold region, a) mainly because of the fluctuations of the light field in the laser mode and b) to a small amount, because the absorption processes due to the laser photons weaken the forward current, which is carried by emission processes, while the absorption noise adds to the emission noise.     

Nonmonotonic temperature dependence of the Hall resistance of a 2D electron system in silicon

For a 2D electron system in silicon, the temperature dependence of the Hall resistance ρ_xy(T) is measured in a weak magnetic field in the range of temperatures (1–35 K) and carrier concentrations n where the diagonal resistance component exhibits a metallic-type behavior. The temperature dependences ρ_xy(T) obtained for different n values are nonmonotonic and have a maximum at T_max ～ 0.16T_F. At lower temperatures T < T_max, the change δρ_xy(T) in the Hall resistance noticeably exceeds the interaction quantum correction and qualitatively agrees with the semiclassical model, where only the broadening of the Fermi distribution is taken into account. At higher temperatures T > T_max, the dependence ρ_xy(T) can be qualitatively explained by both the temperature dependence of the scattering time and the thermal activation of carriers from the band of localized states.     

Thermoelectric effect in the Kondo dot side-coupled to a Majorana mode

We investigate the linear thermoelectric response of an interacting quantum dot side-coupled by one of two Majorana modes hosted by a topological superconducting wire. We employ the numerical renormalization group technique to obtain the thermoelectrical conductance L in the Kondo regime while the background temperature T, the Majorana-dot coupling Γ _m , and the overlap ε _m between the two Majorana modes are tuned. We distinguish two transport regimes in which L displays different features: the weak- (Γ _m <T _K ) and strong-coupling (Γ _m >T _K ) regimes, where T _K is the Kondo temperature. For an infinitely long nanowire where the Majorana modes do not overlap (ε _m = 0), the thermoelectrical conductance in the weak-coupling regime exhibits a peak at T ~ Γ _m <T _K . This peak is ascribed to the anti-Fano resonance between the asymmetric Kondo resonance and the zero-energy Majorana bound state. In the strong-coupling regime, on the other hand, the Kondo-induced peak in L is affected by the induced Zeeman splitting in the dot. For finite but small overlap (0 <ε _m <Γ _m ), the interference between the two Majorana modes restores the Kondo effect in a smaller energy scale Γ′ _m and gives rise to an additional peak in Γ ~ Γ′ _m, whose sign is opposite to that at T ~ Γ _m . In the strong-coupling regime this additional peak can cause a non-monotonic behavior of L with respect to the dot gate. Finally, in order to identify the fingerprint of Majorana physics, we compare the Majorana case with its counterpart in which the Majorana bound states are replaced by a (spin-polarized) ordinary bound state and find that the thermoelectric features for finite ε _m are the genuine effect of the Majorana physics.     

Special features of the <Emphasis Type="Italic">K</Emphasis> = 0 channel in nuclear fission

The opinion that the K = 0 fission channel is completely closed if the spin J and the parity π of the nucleus undergoing fission do not satisfy the condition (?1) ^J = π is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and π values such that they satisfy the condition (?1) ^J = π. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.