Statistical Mechanics for Weak Measurements and Quantum Inseparability

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.

(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.

The Time Division Multi-Channel Communication Model and the Correlative Protocol Based on Quantum Time Division Multi-Channel Communication

Based on the classical time division multi-channel communication theory, we present a scheme of quantum time- division multi-channel communication （QTDMC）. Moreover, the model of quantum time division switch （QTDS） and correlative protocol of QTDMC are proposed. The quantum bit error rate （QBER） is analyzed and the QBER simulation test is performed. The scheme shows that the QTDS can carry out multi-user communication through quantum channel, the QBER can also reach the reliability requirement of communication, and the protocol of QTDMC has high practicability and transplantable. The scheme of QTDS may play an important role in the establishment of quantum communication in a large scale in the future.

Cryptanalysis and Improvement of Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations

In a recent paper [Yan F L et al. Chin.Phys.Lett. 25（2008）1187], a quantum secret sharing the protocol between multiparty and multiparty with single photons and unitary transformations was presented. We analyze the security of the protocol and find that a dishonest participant can eavesdrop the key by using a special attack. Finally, we give a description of this strategy and put forward an improved version of this protocol which can stand against this kind of attack.

Cryptanalysis of an Improved Flexible Ping-Pong Protocol in Perfect and Imperfect Quantum Channels

We recently proposed a flexible quantum secure direct communication protocol [Chin. Phys. Lett. 23 （2006） 3152]. By analyzing its security in the perfect channel from the aspect of quantum information theory, we find that an eavesdropper is capable of stealing all the information without being detected. Two typical attacks are presented to illustrate this point. A solution to this loophole is also suggested and we show its powerfulness against the most general individual attack in the ideal case. We also discuss the security in the imperfect case when there is noise and loss.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Six-State Quantum Key Distribution Using Photons with Orbital Angular Momentum

A new implementation of high-dimensional quantum key distribution （QKD） protocol is discussed. Using three mutual unbiased bases, we present a d？level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.

Implementing a Multi-Qubit Quantum Phase Gate Encoded by Photonic Qubit

A protocol is proposed to implement a three-qubit phase gate for photonic qubits in a three-mode cavity. The idea can be extended to directly implement a N-qubit phase gate. We also show that the interaction time remains unchanged with the increasing number of qubits. In addition, the influence of cavity decay and atomic spontaneous emission on the gate fidelity and photon loss probability is also discussed by numerical calculation.

Entanglement Purification for Mixed Entangled Quantum Dot States via Superconducing Transmission Line Resonators

An entanglement purification protocol for mixed entangled states is presented via double quantum dot molecules inside a superconducing transmission line resonator （TLR）. In the current scenario, coupling for arbitrary double quantum dot molecules can be tuned via the TLR in the large detuning region by controlling the qubit level splitting. The TLR is always empty and only virtually excited, so the interaction is insensitive to both the TLR decay and thermal field. Discussion about the feasibility of our scheme shows that the entanglement purification can be implemented with high fidelity and successful probability.

Superconducting quantum bits

Superconducting quantum bits （qubits） and circuits are the leading candidate for the implementation of solid-state quantum computation. They have also been widely used in a variety of studies of quantum physics, atomic physics, quantum optics, and quantum simulation. In this article, we will present an overview of the basic principles of the superconducting qubits, including the phase, flux, charge, and transmon （Xmon） qubits, and the progress achieved so far concerning the improvements of the device design and quantum coherence property. Experimental studies in various research fields using the superconducting qubits and circuits will be briefly reviewed.

Population Swap of a Pair of Quantum Dots Coupling to a Plasmonic Nanocavity

We theoretically design a single-mode plasmonic ring nanocavity. Based on the plasmonic cavity, the exciton dynamics between two identical quantum dots （QD-p, QD-q） coupled to the nanocavity are investigated. It is shown that the coupling factors gi （i = p, q） between QD-i and surface plasmons are both equal to 12.53meV in our model and exeiton population swap between the two QDs can be realized. The periods and amplitudes of population oscillations can be modified by the coupling factors. Our results may have potential applications in quantum information and quantum computation on a chip.

Universal Quantum Cloning Machine in Circuit Quantum Electrodynamics

We propose a scheme for realizing the 1 → 2 universal quantum cloning machine （UQCM） with superconducting quantum interference device （SQUID） qubits in circuit quantum electrodynamics （circuit QED）. In this scheme, in order to implement UQCM, we only need phase shift gate operation on SQUID qubits and the Raman transitions. The cavity number we need is only one. Thus our scheme is simple and has advantages in the experimental realization. Furthermore, both the cavity and the SQUID qubits are virtually excited, so the decoherence can be neglected.

Quantum Swap Gate with Molecular Ensembles via Cavity Quantum Electrodynamics

We present a simple method to realize a swap gate at one step with two molecular ensembles in a stripline cavity. In this scheme, we can benefit from the enhancement of the coherent coupling and acquire a long coherent time with encoding qubits in different spin states of the rotational ground state in the molecular ensembles. As a by-product, a scheme to create an entangled state with one excitation stored in two ensembles is proposed.

General Theory of Decoy-State Quantum Cryptography with Dark Count Rate Fluctuation

The existing theory of decoy-state quantum cryptography assumes that the dark count rate is a constant, but in practice there exists fluctuation. We develop a new scheme of the decoy state, achieve a more practical key generation rate in the presence of fluctuation of the dark count rate, and compare the result with the result of the decoy-state without fluctuation. It is found that the key generation rate and maximal secure distance will be decreased under the influence of the fluctuation of the dark count rate.

Quantum Correlation Coefficients for Angular Coherent States

Quantum covariance and correlation coefficients of angular or SU（2） coherent states are directly calculated for all irreducible unitary representations. These results explicitly verify that the angular coherent states minimize the Robertson-Schrodinger uncertainty relation for all spins, which means that they are the so-called intelligent states. The same results can be obtained by the Schwinger representation approach.

Quantum computational advantage via 60-qubit 24-cycle random circuit sampling

To ensure a long-term quantum computational advantage,the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares.Here,we demonstrate a superconducting quantum computing systems Zuchongzhi 2.1,which has 66 qubits in a two-dimensional array in a tunable coupler architecture.The readout fidelity of Zuchongzhi 2.1 is considerably improved to an average of 97.74%.The more powerful quantum processor enables us to achieve larger-scale random quantum circuit sampling,with a system scale of up to 60 qubits and 24 cycles,and fidelity of FXEB=(3·66±0·345)×10^(-4).The achieved sampling task is about 6 orders of magnitude more difficult than that of Sycamore[Nature 574,505(2019)]in the classic simulation,and 3 orders of magnitude more difficult than the sampling task on Zuchongzhi 2.0[arXiv:2106.14734(2021)].The time consumption of classically simulating random circuit sampling experiment using state-of-the-art classical algorithm and supercomputer is extended to tens of thousands of years(about 4·8×104years),while Zuchongzhi 2.1 only takes about 4.2 h,thereby significantly enhancing the quantum computational advantage.

Transformation Operator and Criterion for Perfectly Teleporting Arbitrary Three-Qubit State with Six-Qubit Channel and Bell-State Measurement

Using the method presented recently [Phys.Rev.A 77（2008）014306; Phys.Lett.A 369（2007）377], the transformation operator （TO） is explicitly given for teleporting an arbitrary three-qubit state with a six-qubit channel and Bell-state measurements. A criterion on whether such quantum teleportation can be perfectly realized is educed in terms of TO. Moreover, six instantiations on TO and criterion are concisely shown.

Phase Transitions Governed by the Fifth Power of the Golden Mean and Beyond

In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio φ respectively its fifth power φ5. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (IRT) including explanations of cosmological relevance, the ε-infinity theory, superconductivity, and the Tammes problem of the largest diameter of N non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, Fibonacci anyons proposed for topological quantum computation (TQC) were briefly described in comparison to the recently formulated reverse Fibonacci approach using the Janičko number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.

Relation between Characteristic Function of Density Operator and Tomogram

In terms of the intermediate coordinate-momentum representation （Chin. Phys. Lett. 18 （2001） 850） and using the technique of integration within an ordered product of operators, we put the tomography theory into operator version. We reveal the new relation between the tomogram and the characteristic function of the density operator. The new expansion of the density operator in terms of the intermediate coordinate-momentum representation is also obtained.

Bidirectional Mapping between a Biphoton Polarization State and a Single-Photon Two-Qubit State

How to manipulate （operate or measure） single photons efficiently and simply is the basic problem in optical quantum information processing. We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes. This single-photon state carries both the information of the controlled and target photons. It will make the realization of bipartite positive- operator-valued measurements efficiently and simply. Moreover, the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed. Using both the transformations, the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer. All the schemes are feasible with the current experimental technology.