Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given,and the properties ofconditional entropy are investigated.

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Conditional Events and Quantum Logic

This paper begins with an overview of quantum mechanics, and then recounts a relatively recent algebraic extension of the Boolean algebra of probabilistic events to “conditional events” (order pairs of events). The main point is to show that a so-called “superposition” of two (or more) quantum events (usually with mutually inconsistent initial conditions) can be represented in this algebra of conditional events and assigned a consistent conditional probability. There is no need to imagine that a quantum particle can simultaneously straddle two inconsistent possibilities.

Simple Scheme for Realizing the General Conditional Phase Shift Gate and a Simulation of Quantum Fourier Transform in Circuit QED

We propose a theoretical scheme for realizing the general conditional phase shift gate of charge qubits situated in a high-Q superconducting transmission line resonator. The phase shifting angle can be tuned from 0 to 27r by simply adjusting the qubit-resonator detuning and the interaction time. Based on this gate proposal, we give a detailed procedure to implement the three-qubit quantum Fourier transform with circuit quantum eleetrodynamics （QED）. A careful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using current circuit QED techniques.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

Performance analysis of continuous-variable measurement-device-independent quantum key distribution under diverse weather conditions

The effects of weather conditions are ubiquitous in practical wireless quantum communication links.Here in this work,the performances of atmospheric continuous-variable measurement-device-independent quantum key distribution(CV-MDI-QKD)under diverse weather conditions are analyzed quantitatively.According to the Mie scattering theory and atmospheric CV-MDI-QKD model,we numerically simulate the relationship between performance of CV-MDI-QKD and the rainy and foggy conditions,aiming to get close to the actual combat environment in the future.The results show that both rain and fog will degrade the performance of the CV-MDI-QKD protocol.Under the rainy condition,the larger the raindrop diameter,the more obvious the extinction effect is and the lower the secret key rate accordingly.In addition,we find that the secret key rate decreases with the increase of spot deflection distance and the fluctuation of deflection.Under the foggy condition,the results illustrate that the transmittance decreases with the increase of droplet radius or deflection distance,which eventually yields the decrease in the secret key rate.Besides,in both weather conditions,the increase of transmission distance also leads the secret key rate to deteriorate.Our work can provide a foundation for evaluating the performance evaluation and successfully implementing the atmospheric CV-MDI-QKD in the future field operation environment under different weather conditions.

High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.

Tailoring Classical Conditioning Behavior in TiO_(2) Nanowires:ZnO QDs-Based Optoelectronic Memristors for Neuromorphic Hardware

Neuromorphic hardware equipped with associative learn-ing capabilities presents fascinating applications in the next generation of artificial intelligence.However,research into synaptic devices exhibiting complex associative learning behaviors is still nascent.Here,an optoelec-tronic memristor based on Ag/TiO_(2) Nanowires:ZnO Quantum dots/FTO was proposed and constructed to emulate the biological associative learning behaviors.Effective implementation of synaptic behaviors,including long and short-term plasticity,and learning-forgetting-relearning behaviors,were achieved in the device through the application of light and electrical stimuli.Leveraging the optoelectronic co-modulated characteristics,a simulation of neuromorphic computing was conducted,resulting in a handwriting digit recognition accuracy of 88.9%.Furthermore,a 3×7 memristor array was constructed,confirming its application in artificial visual memory.Most importantly,complex biological associative learning behaviors were emulated by mapping the light and electrical stimuli into conditioned and unconditioned stimuli,respectively.After training through associative pairs,reflexes could be triggered solely using light stimuli.Comprehen-sively,under specific optoelectronic signal applications,the four features of classical conditioning,namely acquisition,extinction,recovery,and generalization,were elegantly emulated.This work provides an optoelectronic memristor with associative behavior capabilities,offering a pathway for advancing brain-machine interfaces,autonomous robots,and machine self-learning in the future.

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.

About the Nature of the Quantum System—An Examination of the Random Discontinuous Motion Interpretation of the Quantum Mechanics

What is the quantum system? Consider the wave-function of the electron—what we call “single particle wave-function”—and assume that it contains N wave-packets. If we pass all the wave-packets through an electric field, all are deflected, as if each one of them contains an electron. However, if we bring any two wave-packets to travel close to one another, they don’t repel one another, as if at least one of them contains no charge. In trying to solve the measurement problem of the quantum mechanics (QM), different interpretations were proposed, each one coming with a particular ontology. However, only one interpretation paid explicit attention to the contradiction mentioned above. This interpretation was proposed by S. Gao who named it “random discontinuous motion” (RDM), because it assumes the existence of a particle that jumps from place to place at random. The particle carries all the physical properties of the respective type of particle, mass, charge, magnetic momentum, etc. It jumps under the control of an “instantaneous condition” about which Gao did not give details so far. Along with presenting problems of the QM that this interpretation solves, this text reveals difficulties vis-à-vis entanglements and the special relativity.

MODIFICATION OF ABSORPTION SPECTRUM OF GaAs/AlGaAs QUANTUM WELL INFRARED PHOTODETECTOR BY POSTGROWTH ADJUSTMENT

Quantum well intermixing techniques modify the geometric shape of quantum wells to allow postgrowth adjustments.The tuning effect on the optical response property of a GaAs/AlGaAs quantum well infrared photodetector(QWIP) induced by the interdifussion of Al atoms was studied theoretically.By assuming an improvement of the heterointerface quality and an enhanced Al interdiffusion caused by postgrowth intermixings,the photoluminescence spectrum shows a blue-shifted,narrower and enhanced photoluminescence peak.The infrared optical absorption spectrum also shows the expected redshift of the response wavelength.However,the variation in the absorption peak intensity depends on the boundary conditions of the photo generated carriers.For high-quality QWIP samples,the mean free path of photocarriers is long so that the photocarriers are largely coherent when they transport across quantum wells.In this case,the enhanced Al interdiffusion can significantly degrade the infrared absorption property of the QWIP.Special effects are therefore needed to maintain and/or improve the optical properties of the QWIP device during postgrowth treatments.

QUANTUM MECHANICAL MODEL AND SIMULATION OF GaAs/AlGaAs QUANTUM WELL INFRARED PHOTODETECTOR-Ⅱ ELECTRICAL ASPECTS

A complete quantum mechanical model for GaAs/AlGaAs quantum well infrared photodetectors(QWIPs) was presented. The photocurrent was investigated by the optical transition(absorption coefficient)between the ground state and the excited states due to the nonzero component of the radiation field along the sample growth direction. By studying the inter diffusion of the Al atoms across the GaAs/AlGaAs heterointer faces, the mobility of the drift diffusion carriers in the excited states was calculated. As a result, the measurement results of the dark current and the photocurrent spectra are explained theoretically.

Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.

A Novel Exact Fixed-node Quantum Monte Carlo Algorithm

In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is optimized synchronistically in the diffusion procedure, but not before the beginning of EFNQMC computation. In order to optimize the trial function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton and converges super linearly. We also use a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 11 A1 state of CH2, 1Ag state of C8 and the ground-states of H2, LiH, Li2, H2O, respectively. The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.

A Noise-Robust Pulse for Excitation Transfer in a Multi-Mode Quantum Memory

Multi-mode quantum memory is a basic element required for long-distance quantum communication,as well as scalable quantum computation.For on-demand readout and long storage times,control pulses are crucial in order to transfer atomic excitations back and forth into spin excitations.Here,we introduce noise-robust composite pulse sequences for high-fidelity excitation transfer in multi-mode quantum memory.These pulses are robust to the deviations in amplitude and the detuning parameters of realistic conditions.We show the efficiency of these composite pulses with a typical rare-earth ion-doped system.This approach could be applied to a variety of quantum memory schemes.

Quantum Secure Direct Communication with Five-Qubit Entangled State

Recently,a genuine five-qubit entangled state has been achieved by Brown et al.[J.Phys.A 38(2005)1119].Later it was indicated that this state can be used for quantum teleportation and quantum state sharing.Here we build a quantum secure direct communication protocol with this state,and prove that it is secure in ideal conditions.In the protocol,the sender performs unitary transformations to encode a secret message on his/her particles and sends them to the receiver.The receiver then performs projective determinate measurement to decode the secret message directly.Fhrthermore,this protocol utilizes superdense coding to achieve a high intrinsic efficiency and source capacity.

Quantum Computing via Singlet-Triplet Spin Qubits in Nanowire Double Quantum Dots

We propose a new structure for quantum computing via spin qubits with high fidelity.Each spin qubit corresponds to two electrons in a nanowire double quantum dot,with the singlet and one of the triplets as the logical qubit states.The entangling gate is effected by virtual charge dipole transitions.We include noise to show the feasibility of this scheme under current experimental conditions.

Testing Quantum Entanglement with Local Measurement

We propose to detect quantum entanglement by a condition of local measurements.We find that this condition can efficiently detect the pure entangled states for both discrete and continuous variable systems.It does not depend on interference of decoherence from noise and detection loss in some systems,which allows a loophole-free test in real experiments.In particular,it is a necesary condition for the violation of some generalized Bell inequalities.

Steered coherence and entanglement in the Heisenberg XX chain under twisted boundary conditions

We study steered coherence(SC)and entanglement in a three-spin Heisenberg XX model under twisted boundary conditions and show that their strengths can be significantly enhanced by tuning the twist angle.The optimal twist angleθ_(opt)for achieving the maximum l_(1) norm of SC isπin the region of weak field B and decreases gradually fromπto 0 when B increases after a critical value,while for the relative entropy of SC,θ_(opt)equalsπin the weak field region and 0 otherwise.The entanglement and the critical temperature above which the entanglement vanishes can also be significantly enhanced by tuning the twist angle from 0 toπ.

Effect of spin on the instability of THz plasma waves in field-effect transistors under non-ideal boundary conditions

Terahertz(THz) radiation can be generated due to the instability of THz plasma waves in field-effect transistors(FETs). In this work, we discuss the instability of THz plasma waves in the channel of FETs with spin and quantum effects under non-ideal boundary conditions. We obtain a linear dispersion relation by using the hydrodynamic equation, Maxwell equation and spin equation. The influence of source capacitance, drain capacitance, spin effects, quantum effects and channel width on the instability of THz plasma waves under the non-ideal boundary conditions is investigated in great detail. The results of numerical simulation show that the THz plasma wave is unstable when the drain capacitance is smaller than the source capacitance;the oscillation frequency with asymmetric boundary conditions is smaller than that under non-ideal boundary conditions;the instability gain of THz plasma waves becomes lower under non-ideal boundary conditions. This finding provides a new idea for finding efficient THz radiation sources and opens up a new mechanism for the development of THz technology.