Quantum Collision Research Articles

Improved Quantum Rebound Attacks on Double Block Length Hashing with Round-Reduced AES-256 and ARIA-256

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum collision attacks on hash functions. Their proposal presented a quantum adaptation of the rebound attack and revealed that differential trails, which have too low probability for use in classical settings, might be exploitable in quantum settings. After their work, subsequent research has actively delved into analyzing the security of hash functions in the quantum setting.In this paper, we revisit the quantum rebound attacks on the double block hash function Hirose instantiated with 10-round AES-256 (HCF-AES-256) and 7-round ARIA-256 (HCF-ARIA-256) proposed by Chauhan et al. and Baek et al., respectively. Initially, we identify the flaws in their work and reevaluate the complexity of the attacks. We reveal that the flaws stem from not considering the issue that the S-box differential equation has one solution on average. Earlier research addressed this problem by adding auxiliary bits to the search space. If this method is used to correct the flaws, the resulting time complexities are 217.36 and 220.94 times higher than their proposals. Consequently, in some settings, their attacks become less efficient than generic attacks.Subsequently, we propose improved quantum rebound attacks using nested quantum amplitude amplification and quantum state preparation. Our improved attack efficiently pre-filters the search space, leading to a reduction in overall time complexity. We first classically reduce the search space and employ quantum state preparation to generate a superposition state over the pre-filtered search space. We then use nested quantum amplitude amplification to further reduce the search space quantumly. As a result, we achieve a reduction in the time complexity of the quantum rebound attacks on HCF-AES-256 and HCF-ARIA-256 by factors of 211.2 and 219.5, respectively, making the attacks more efficient than generic attacks again.

Measurability of Wigner time delay in a photoionization experiment

We visit significant historical steps in quantum collision physics that make photoionization time delay measurable, especially considering the time-reversal symmetry in related processes. The works of A. Ravi P. Rau and Ugo Fano inspire key ideas presented in this article.

Ion molecule reaction dynamics for disentangling competing reactive pathways

ABSTRACT Chemical reactions are by definition dynamical. Reactants move towards each other, collide and products separate again. Therefore, it is important to look beyond the stationary description, and look at how molecules rearrange and how energy is partitioned during a reactive collision. Chemical reactions are complex and often involve competing chemical and/or atomistic pathways whose dominance depends on several factors as for example the involved quantum states or collision energy. Here, we focus on ion molecule reactions which play an important role in gaseous environments even though their steady-state abundance is often much lower than that of their neutral counterparts. We present the use of angle and energy differential cross sections from crossed beam imaging experiments to disentangle competing reaction pathways. The general term pathways includes different effects of specific reactant quantum states on the atomistic mechanism to the competition of different product channels.

Improving Entanglement Generation Using the Coherence of a Nonthermal Reservoir

AbstractThe effect of environmental coherence on bipartite and tripartite quantum entanglements using quantum collision models is studied. In the collision model, an open quantum system of two qubits indirectly interacts with the reservoir via auxiliary qubits. The reservoir is modeled as a collection of initially uncorrelated qubits prepared in an identically nonthermal state. It is shown that the coherence of the nonthermal reservoir contributes to the generation and protection of entanglement. It is found that adding coherence to the initial state of the reservoir qubit can significantly enhance the steady‐state entanglement of the system, and the presence of coherence in the reservoir allows steady‐state entanglement to be obtained in a higher temperature region.

Unveiling the Markovian to non-Markovian transition with quantum collision models

The concept of non-Markovianity in open quantum systems is traditionally associated with the existence of information backflows from the environment to the system. Meanwhile, the mechanisms through which such backflows emerge are still a subject of debate. In this work, we use collision models to study memory effects in the dynamics of a qubit system in contact with a thermal bath made up of few ancillas, in which system-ancilla and ancilla–ancilla interactions are considered. In the single-ancilla limit case, we show that the system–bath information flow exhibits an interesting mixture of chaotic and regular oscillatory behavior, which depends on the interaction probabilities. In parallel, our results clearly indicate that the information backflows decrease when new ancillas are added to the bath, which sheds light on the nature of the Markovian to non-Markovian transition.

Wave Function Realization of a Thermal Collision Model.

An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on the quantum collision model. Modeling systems dynamics with wave functions and modeling the interaction with the environment with a collision sequence reduces the scale of the complexity significantly. The algorithm developed can be implemented on quantum computers. We introduce stochastic methods that exploit statistical characteristics of the model such as Markovianity, Brownian motion, and binary distribution. The central limit theorem is employed to study the convergence of distributions of stochastic dynamics of pure quantum states represented by wave vectors. By averaging a sample of functions in the distribution we prove and demonstrate the convergence of the dynamics to the mixed quantum state described by a density operator.

Electron scattering and ionization of astrophysical molecules

Interaction of electrons with cumulene carbenes (H2C2, H2C3, H2C4, H2C5, H2C6) and some of the possible outcomes are reported in this article. The prominent scattering channels like elastic, inelastic, ionization, and momentum transfer are examined through respective cross sections for these molecules and their polyacetylene isomers (C2H2, C4H2, C6H2). The quantum collision problem of the e-target system is solved through the optical potential approach. The optimized structures, ionization energies (IP), and polarizabilities of the target molecules are calculated using the Density Functional Theory. These target parameters are found to be in good agreement with those available from the literature. The computations for cross sections were performed in the energy ranging from the ionization threshold of the targets to 5000 eV. To the best of the authors' knowledge, it is the first time that the cross section values of the above-mentioned molecules are reported. We have established a strong correlation between the maximum ionization cross section and ionization energy as well as polarizability, suggesting the consistency of the results reported here. An investigation into the isomeric effect reveals significant differences in the properties and magnitudes of cross sections of cumulene carbenes compared to polyacetylenes. The present findings would be helpful in astrophysical modelling, spectroscopy, and studying interstellar & circumstellar spaces.

Quantum Collision Models: A Beginner Guide.

In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model.

A Brief Journey through Collision Models for Multipartite Open Quantum Dynamics

The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.

Developing a New Collision-Resistant Hashing Algorithm

Today, cryptographic hash functions have numerous applications in different areas. At the same time, new collision attacks have been developed recently, making some widely used algorithms like SHA-1 vulnerable and unreliable. This article is aiming at the development of a new hashing algorithm that will be resistant to all cryptographic attacks, including quantum collision attacks that potentially pose a threat to some widely used cryptographic hash functions. This algorithm was called Nik-512. The avalanche effect is tested to ensure the cryptographic strength of the developed algorithm. The Nik-512 function is then applied to build a data integrity system which can be used to protect data from malicious users.

Quantum scattering as a work source

We consider a collision between a moving particle and a fixed system, each having internal degrees of freedom. We identify the regime where the motion of the particle acts as a work source for the joint internal system, leading to energy changes which preserve the entropy. This regime arises when the particle has high kinetic energy and its quantum state of motion is broad in momentum and narrow in space, whether pure or mixed. In this case, the scattering map ruling the dynamics of the internal degrees of freedom becomes unitary and equivalent to that of a time-dependent interaction between the internal degrees of freedom of the colliding systems. It follows that the kinetic energy lost by the particle during the autonomous quantum collision coincides with the work performed by the time-dependent interaction. Recently, collisions with particles were shown to act as heat sources under suitable conditions; here we show that they can also act as work sources. This opens interesting perspectives for quantum thermodynamics formulations within scattering theory.

Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in the dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes, forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here, we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to an analytical treatment for a number of timely problems such as the system interaction with two-photon wave packets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.

Stochastic versus Periodic Quantum Collision Models

Most literature on quantum collision models (CMs) usually considers periodic weak collisions featuring a fixed waiting time between two next collisions. Some works have yet addressed CMs with random waiting time and strong collisions (stochastic CMs). This short paper discusses how the open dynamics arising from these two types of models can be formally mapped with one another. This can be achieved for a given stochastic CM by constructing an associated periodic CM such that the waiting time randomness of the former is turned into the mixedness of the ancilla’s initial state of the latter, introducing at the same time an additional state of the ancilla. Through this mapping, non-Markovian behaviour arising from a constrained number of stochatic collisions can be linked to initial ancilla–ancilla correlations of the associated periodic CM.

Measured Composite Collision Models: Quantum Trajectory Purities and Channel Divisibility.

We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and informationally complete measurement on the memory, we study the divisibility of the resulting dynamics in dependence of the measurement strength. The measurements give rise to quantum trajectories of the system and we show that the average asymptotic purity depends on the specific form of the measurement. With the help of numerical simulations, we demonstrate that the different performance of the measurements is generic and holds for almost all interaction gates between the system and the memory in the composite collision model. The discrete model is then extended to a time-continuous limit.

Investigation of Electron Scattering from Vinyl Ether and Its Isomers

This article reports a comprehensive theoretical study of electron scattering from vinyl ether and its isomers. The electron–molecule quantum collision problem is solved through a complex optical potential approach. From the solution of the Schrödinger equation corresponding to this scattering problem, various cross sections were obtained for energies from ionization threshold of target to 5 keV. To deal with the non-spherical and complex structure, a multi-center group additivity approach is used. Furthermore, geometrical screening correction is applied to compensate for the overestimation of results due to electron charge density overlap. We found an interesting correlation between maximum ionization cross section with polarizability and ionization energy of the target molecule. The fitting of the total cross section as a function of the incident electron energy is reported in this article. The correlation between the effective diameter of the target and the projectile wavelength at maximum ionization energy is also reported for vinyl ether and its isomers. The data presented here will be useful to biomedical field, mass spectrometry, and chemical database for military range applications. The cross sections are also important to model Mars’s atmosphere due to their presence in its atmosphere. The gas-kinetic radius and the van der Waals coefficients are estimated from the electron-impact total scattering cross sections. In addition, the current study predicts the presence of isomeric effects in the cross section.

Multipartite Correlations in Quantum Collision Models.

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics.

Anonymous communication protocol over quantum networks

We propose a W state-based protocol for anonymously transmitting quantum messages in a quantum network. Different from the existing protocols [A. Unnikrishnan, et al., Phys. Rev. Lett. 122, 240501 (2019)], the proposed protocol can be effectively implemented in the network only equipped with quantum channels and regular broadcast channels. Throughout the design procedure, we develop three sub-protocols using the W state, including the quantum collision detection protocol and the quantum notification protocol. Moreover, together with the conventional anonymous entanglement protocol, the whole anonymous communication protocol has been constructed. Finally, we examine the correctness and security of the proposed quantum anonymous communication protocol.

Three-dimensional magneto-optical trapping model of CaH molecule based on multi-energy-level rate equation

Laser cooling and magneto-optical trapping of molecules is regarded as one of the state-of-the-art research fields in physics, which possesses broad applications in exploring fundamental physics beyond the Standard Model, quantum many-body physics, cold/ultracold chemistry and collision studies and so forth. Owing to the characteristic of highly diagonal Franck-Condon factors, lower saturation irradiance and larger scattering rate, the CaH molecule has been proposed as a promising candidate for laser cooling and magneto-optical trapping ever since 2004. Taking advantage of the multi-energy-level rate equation as well as the dual frequency effect, we evaluate the damping and trapping forces contained in the optical transitions of <inline-formula><tex-math id="M4">\begin{document}$ {\mathrm{A}}^{2}{\mathrm{Π}}_{1/2}\leftarrow {\mathrm{X}}^{2}{\mathrm{Σ }}^{+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M4.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}${\mathrm{B}}^{2}{\mathrm{Σ }}^{+}\leftarrow {\mathrm{X}}^{2}{\mathrm{Σ }}^{+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M5.png"/></alternatives></inline-formula>, analyze the cooling and trapping performance for different laser polarization sets, power values and detunings of four laser components, and determine the variations in the damping and trapping forces due to an additional frequency component. It is discovered that if the laser polarization is set to be <i>σ</i><sup>-</sup><i>σ</i><sup>+</sup><i>σ</i><sup>+</sup><i>σ</i><sup>+</sup><i>σ</i><sup>+</sup>, the detuning for the second laser component is <i>Γ</i><italic/> while the detuning of other components are set to be -2<i>Γ</i>, and the laser power is set to be 150 mW, one can obtain a damping acceleration of 28000 m/s<sup>2</sup>, and a trapping acceleration of 19000 m/s<sup>2</sup> for the transition of <inline-formula><tex-math id="M6">\begin{document}$ {\mathrm{A}}^{2}{\mathrm{Π}}_{1/2}\leftarrow {\mathrm{X}}^{2}{\mathrm{Σ }}^{+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220304_M6.png"/></alternatives></inline-formula>, both of which reach the optimal values under the current scope of the research and exhibit better performance than the CaF molecule. Our results, on one hand, not only offer an ideal method to comprehend the CaH MOT in theory but also help design the CaH MOT experiment or even achieve the Bose-Einstein condensation (BEC) of cold diatomic molecules. On the other hand, alkaline-earth-metal monohydrides (AEMHs) such as CaH, SrH and BaH are well-known for their permanent electric dipole moment, therefore these trapped diatomic molecules can be utilized to untangle the mechanism of dipole-dipole interaction, thus paving the way to realizing the molecular entanglement and quantum computing. More interestingly, current experimental systems for the non-zero measurement of the electron’s electric dipole moment (eEDM), including ThO, YbF and HfF<sup>+</sup>, still cannot be conducted simultaneously under the laser cooling and magneto-optical trapping technique while maintaining the ease of full polarization and internal co-magnetometry, all of which undoubtedly can increase the coherent measurement time and hence the statistical sensitivity, as well as the immunity to the systematic sensitivity. Previous studies reported that AEMHs share some similar characters with alkaline-earth-metal monofluorides (AEMFs) such as in electron correlation effects, however, the hyperfine energy level structures of AEMHs are relatively simpler than those of AEMFs, and AEMHs are prone to being polarized under the externally applied electric field. All of these lead to the trend that AEMHs may possess the dual character that it can be not only laser cooled and trapped in a MOT but also adopted as an candidate to measure the eEDM. Therefore, our work lays a substantial foundation for the theoretical and experimental study of SrH and BaH that inevitably will contribute to the exploration of the CP violation and new physics beyond the Standard Model on a scientific platform based on cold polar molecules, which is obviously different from large facilities such as the Large Hadron Collider.

Quantum rebound attack to D-M structure based on ARIA algorithm

With the increasing application of quantum computing, quantum technology is increasingly used in the security analysis and research of multiple symmetric cryptographic algorithms such as block ciphers and hash functions. In 2020, Sasaki et al. proposed a dedicated quantum collision attack against hash functions in EUROCRYPT. Some differential trajectories with a probability of 2−2n/3 that cannot be used in the classical environment may be used to launch collision attacks in the quantum environment. The ARIA algorithm is a block cipher proposed by the Korean researcher Kwon et al. on ICISC 2003. The block cipher algorithm is similar to AES in structure. This article mainly analyzes the security of Davies-Meyer structure, and uses AIRA as the permutation function to construct ARIA hash function based on the DM hash model. A new AIRA differential path was found based on MILP, and 7 rounds of ARIA-DM hash function quantum rebound attacks were given.

Collisional strong-field QED kinetic equations from first principles

Starting from nonequilibrium quantum field theory on a closed time path, we derive kinetic equations for the strong-field regime of quantum electrodynamics (QED) using a systematic expansion in the gauge coupling $e$. The strong field regime is characterized by a large photon field of order $\mathcal{O}(1/e)$, which is relevant for the description of, e.g., intense laser fields, the initial stages of off-central heavy ion collisions, and condensed matter systems with net fermion number. The strong field enters the dynamical equations via both quantum Vlasov and collision terms, which we derive to order $\mathcal{O}(e^2)$. The kinetic equations feature generalized scattering amplitudes that have their own equation of motion in terms of the fermion spectral function. The description includes single photon emission, electron-positron pair photoproduction, vacuum (Schwinger) pair production, their inverse processes, medium effects and contributions from the field, which are not restricted to the so-called locally-constant crossed field approximation. This extends known kinetic equations commonly used in strong-field QED of intense laser fields. In particular, we derive an expression for the asymptotic fermion pair number that includes leading-order collisions and remains valid for strongly inhomogeneous fields. For the purpose of analytically highlighting limiting cases, we also consider plane-wave fields for which it is shown how to recover Furry-picture scattering amplitudes by further assuming negligible occupations. Known on-shell descriptions are recovered in the case of simply peaked ultrarelativistic fermion occupations. Collisional strong-field equations are necessary to describe the dynamics to thermal equilibrium starting from strong-field initial conditions.