Deduction, Ordering, and Operations in Quantum Logic

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a, substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed.     

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.     

Bright 547-dimensional Hilbert-space entangled resource in 28-pair modes biphoton frequency comb from a reconfigurable silicon microring resonator

High-dimensional entanglement provides valuable resources for quantum technologies,including quantum communication,quantum optical coherence tomography,and quantum computing.Obtaining a high brightness and dimensional entanglement source has significant value.Here we utilize a tunable asymmetric Mach–Zehnder interferometer coupled silicon microring resonator with 100 GHz free spectral range to achieve this goal.With the strategy of the tunable coupler,the dynamical and extensive tuning range of quality factors of the microring can be obtained,and then the biphoton pair generation rate can be optimized.By selecting and characterizing 28 pairs from a more than 30-pair modes biphoton frequency comb,we obtain a Schmidt number of at least 23.4 and on-chip pair generation rate of 19.9 MHz/m W;under a low on-chip pump power,which corresponds to 547 dimensions Hilbert space in frequency freedom.These results will prompt the wide applications of quantum frequency comb and boost the further large density and scalable on-chip quantum information processing.     

Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiled through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise.     

A two-step quantum secure direct communication protocol with hyperentanglement

We propose a two-step quantum secure direct communication (QSDC) protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol.     

A Simplified Quantum Logic Network for Unambiguous Discrimination of Two Nonlocal and Unknown Pure Qubit States

Two nonlocal and unknown pure qubit states can, with a certain probability of success, be discriminated unambiguously with the aid of local operations, classical communication, and shared entanglements (LOCCSE). We present a scheme for such kind of nonlocal unambiguous quantum state discrimination. This scheme consists of a nonlocal positive operator valued measurement (POVM). This nonlocal POVM can be realized by performing nonlocal unitary operations on initial system and ancillary qubits, and local von Neumann projective measurements on the ancilla plus initial system. By utilizing the degrees of freedom of the original system Hilbert space, we need far more simpler operations than those required by the original Neumark approach. We construct a quantum logic network to implement the required nonlocal POVM.     

A short introduction to quantum symmetry

In quantum theory, symmetries more general than groups are possible. We give a general definition of a quantum symmetry, such that symmetry operations act on the Hilbert space of physical states and notions of unitarity, invariance and covariance are defined. Within this frame, weak quasi quantum groups are described as a natural generalization of group algebras. Consistency with locality distinguishes them from more general quantum symmetries. To find the new kinds of symmetry one should investigate low dimensional quantum systems such as two-dimensional layers.     

Control of trapped-ion quantum states with optical pulses

We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped-ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways--one that makes the system completely uncontrollable and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schr?dinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.     

Deconstructing non-dissipative non-Dirac-Hermitian relativistic quantum systems

A method to construct non-dissipative non-Dirac-Hermitian relativistic quantum system that is isospectral with a Dirac-Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-Hermitian operators, which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-Hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetry.     

Quantum entanglement in a two—dimensional ion trap

In this paper,we investigate the quantum entanglement in a two-dimensional ion trap system.we discuss the quantum entanglement between the ion and phonons by using reduced entropy,and that between two degrees of freedom of the vibrational motion along x and y directions by using quantum relative entropy.We discuss also the influence of initial state of the system on the quantum entanglement and the relation between two entanglements in the trapped ion system.     

Note on Generalized Quantum Gates and Quantum Operations

Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ. This subject is supported by NSF of China (10571113).     

基于轨道角动量的多自由度W态纠缠系统

提出了一种制备三光子纠缠W态的方案, 该方案利用携带轨道角动量为lħ的光子(其中l可取(-∞, +∞)的任意整数)可构成无穷维向量空间的特性, 采用两种类型的参量下转换, 产生轨道角动量-自旋角动量纠缠的两对光子和一对偏振纠缠光子, 通过纠缠交换制备三光子多自由度的W态, 实现三光子体系纠缠的高维度、大容量量子信息处理. 方案采用q-plate相位光学器件和单模光纤等器件制备两个不同自由度(轨道角动量与偏振)混合的W态, 并利用计算机全息相位图改进方案制备三个不同自由度(轨道角动量、线动量和偏振)混合的W态. 本方案可稳定产生两种等概率互为对称的W态, 具有高维度、强纠缠特性与抗比特丢失能力, 信息量达log₂^m+2比特(m为l的可取值个数), 有望实现可扩容量子比特的安全通信.     

Optical hybrid approaches to quantum information

This article reviews recent hybrid approaches to optical quantum information processing, in which both discrete and continuous degrees of freedom are exploited. There are well‐known limitations to optical single‐photon‐based qubit and multi‐photon‐based qumode implementations of quantum communication and quantum computation, when the toolbox is restricted to the most practical set of linear operations and resources such as linear optics and Gaussian operations and states. The recent hybrid approaches aim at pushing the feasibility, the efficiencies, and the fidelities of the linear schemes to the limits, potentially adding weak or measurement‐induced nonlinearities to the toolbox.     

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.     

Scheme for implementing quantum dense coding with four-particle decoherence-free states in an ion trap

This paper proposes an experimentally feasible scheme for implementing quantum dense coding of trapped-ion system in decoherence-free states. As the phase changes due to time evolution of components with different eigenenergies of quantum superposition are completely frozen, quantum dense coding based on this model would be perfect. The scheme is insensitive to heating of vibrational mode and Bell states can be exactly distinguished via detecting the ionic state.     

Lattice Wess-Zumino-Witten model and quantum groups

Quantum groups play the role of symmetries of integrable theories in two dimensions. They may be detected on the classical level as Poisson-Lie symmetries of the corresponding phase spaces. We discuss specifically the Wess-Zumino-Witten conformally invariant quantum field model combining two chiral parts which describe the left- and right-moving degrees of freedom. On one hand, the quantum group plays the role of the symmetry of the chiral components of the theory. On the other hand, the model admits a lattice regularization (in Minkowski space) in which the current algebra symmetry of the theory also becomes quantum, providing the simplest example of a quantum group symmetry coupling space-time and internal degrees of freedom. We develop a free field approach to the representation theory of the lattice sl (2)-based current algebra and show how to use it to rigorously construct an exact solution of the quantum SL (2) WZW model on lattice.     

Emergent Newtonian dynamics and the geometric origin of mass

We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples.     

Quantum Versus Stochastic Processes and the Role of Complex Numbers

We argue that the complex numbers are an irreducible object of quantum probability: this can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having the complex phases as primitive ingredient implies that we need to accept nonadditive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes: they are characterized by the introduction of a density matrix on phase space paths (it thus includes phase information) and fully reproduces quantum mechanical predictions. We can write quantum differential equations (in analogy to Langevin equation) that could be interpreted as referring to individual quantum systems. We describe the reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. We discuss the relevance of our results for the interpretation of quantum theory (a sample space is possible if probabilities are nonadditive) and quantum gravity (the Hilbert space arises here after the consideration of a background causal structure).     

Quaternionic quantum field theory

We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation. The theory takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.     

Quantum Algorithms in Hilbert Database

A fast quantum algorithm for a search and pattern recognition in a Hilbert space memory structure is proposed. All the memory information is mapped onto a unitary operator acting upon a quantum state which represents a piece of information to be retrieved. As a result of only one quantum measurement, the address of the required information encoded in a number of the corresponding row of the unitary matrix is determined. By combining direct and dot products, the dimensionality of the memory space can be made exponentially large, using only linear resources. However, since the preprocessing, i.e., mapping the memory information into a Hilbert space can appear to be exponentially expensive, the proposed algorithm will be effective for NASA applications when the preprocessing is implemented on the ground, while the memory search is performed on remote objects.