Classical-Operation-Based Deterministic Secure Quantum Communication

We generalize the unitary-operation-based deterministic secure quantum communication (UODSQC) model (protocol) to describe the conventional deterministic secure quantum communication (DSQC) protocols in which unitary operations are usually utilized for encoding or decoding message. However, it is found that unitary operation for message encoding or decoding is not required and can be replaced with classical operation in DSQC. So the classical-operation-based deterministic secure quantum communication (CODSQC) model (protocol) is put forward. Then the rigorous mathematical analysis to explain the reason why classical operations can replace unitary operations to encode or decode secret deterministic message is given. Although unitary operations are still possibly needed in the whole communication of CODSQC model (protocol), those used for message encoding or decoding are omitted and replaced with classical operations in CODSQC model (protocol). As a result, the CODSQC model (protocol) is simpler and even more robust than the UODSQC one.     

Probabilistic Process Algebra to Unifying Quantum and Classical Computing in Closed Systems

We have unified quantum and classical computing in open quantum systems called qACP which is a quantum generalization of process algebra ACP. But, an axiomatization of quantum and classical processes with an assumption of closed quantum systems is still missing. For closed quantum systems, unitary operator, quantum measurement and quantum entanglement are three basic components of quantum computing. This leads to probability unavoidable. Along the solution of qACP to unify quantum and classical computing in open quantum systems, we unify quantum and classical computing with an assumption of closed systems under the framework of ACP-like probabilistic process algebra. This unification make it can be used widely in verification of quantum and classical computing mixed systems, such as most quantum communication protocols.

     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution on oceanic quantum channels

Simultaneous two-way classical and quantum (STCQ) communication combines both continuous classical coherent optical communication and continuous-variable quantum key distribution (CV-QKD), which eliminates all detection-related imperfections by being measurement-device-independent (MDI). In this paper, we propose a protocol relying on STCQ communication on the oceanic quantum channel, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and the classical communication ciphertext. We analyse the encoding combination in classical communication and consider the probability distribution transmittance under seawater turbulence with various interference factors. Our numerical simulations of various practical scenarios demonstrate that the proposed protocol can simultaneously enable two-way classical communication and CV-MDI QKD with just a slight performance degradation transmission distance compared to the original CV-MDI QKD scheme. Moreover, the asymmetric situation outperforms the symmetric case in terms of transmission distance and optical modulation variance. We further take into consideration the impact of finite-size effects to illustrate the applicability of the proposed scheme in practical scenarios. The results show the feasibility of the underwater STCQ scheme, which contributes toward developing a global quantum communication network in free space.     

Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness

So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this Letter, we present a stochastic model with time-correlated noise that exactly reproduces any unitary evolution of a qubit and requires just four classical states. The invasive updating of only 1 bit during a measurement accounts for the quantum violation of the Leggett-Garg inequalities. Unlike in a pilot-wave theory, the stochastic forces governing the jumps among the four states do not depend on the quantum state but only on the unitary evolution. This model is used to derive a local hidden variable model, augmented by 1 bit of classical communication, for simulating entangled Bell states.     

Local distinguishability of multipartite unitary operations

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicates that the lost identity of a nonlocal unitary operation can be recovered locally. No entanglement between distant parties is required.     

Distilling Gaussian states with Gaussian operations is impossible

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.     

A Hierarchical Modulation Coherent Communication Scheme for Simultaneous Four-State Continuous-Variable Quantum Key Distribution and Classical Communication

We present a hierarchical modulation coherent communication protocol, which simultaneously achieves classical optical communication and continuous-variable quantum key distribution. Our hierarchical modulation scheme consists of a quadrature phase-shifting keying modulation for classical communication and a four-state discrete modulation for continuous-variable quantum key distribution. The simulation results based on practical parameters show that it is feasible to transmit both quantum information and classical information on a single carrier. We obtained a secure key rate of \(10^{-3}\) bits/pulse to \(10^{-1}\) bits/pulse within 40 kilometers, and in the meantime the maximum bit error rate for classical information is about \(10^{-7}\). Because continuous-variable quantum key distribution protocol is compatible with standard telecommunication technology, we think our hierarchical modulation scheme can be used to upgrade the digital communication systems to extend system function in the future.     

Feedback in the problem of distinguishing between two nonorthogonal coherent states

Feedback is proposed for distinguishing between two weak coherent states with phases differing by ∼π. The mutual nonorthogonality of such states gives rise to a discrimination error, which can be reduced by using feedback. An optical quantum channel is discussed where the input is classical information encoded in two weak coherent states. For a channel with feedback, the discrimination error probability is calculated, and the mutual entropy that quantifies the fidelity between input and output is evaluated. We find that the use of a feedback loop in a quantum communication channel can increase the mutual entropy when canonical position or photon number is measured.     

Efficient Entanglement Concentration Schemes for Separated Nitrogen-Vacancy Centers Coupled to Low-Q Microresonators

We present several efficient entanglement concentration protocols (ECPs) with the nitrogen-vacancy (N-V) centers coupled to low-Q microresonators. Based on the input-output process of ancillary coherent light pulse in low-Q microresonators, we can obtain the maximally entangled states among remote participants via local operations and classical communication. Our protocols use a conventional photon detector to discriminate the two coherent states |α〉 and |?α〉, which is more convenient than homodyne measurement. We discuss the feasibility of our protocols, and they may be beneficial for quantum repeaters and quantum information processing.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltoniansystems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other istime-dependent Hamiltonian system. The quantum unitary operatorrelevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

Implementation of nonlocal quantum swap operation on two entangled pairs

We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs.We discuss the resources of the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation.We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel.The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.     

Unitary transformations can be distinguished locally

We show that, in principle, N-partite unitary transformations can be perfectly discriminated under local operations and classical communication despite their nonlocal properties. Based on this result, some related topics, including the construction of the appropriate quantum circuit together with the extension to general completely positive trace preserving operations, are discussed.     

Properties of Entropy and Entanglement of Two-Mode Nonlinear Coherent States

In this communication, two-mode nonlinear coherent states are reviewed and special cases are given.Starting from a three-level atom coupled to two modes of radiation with any form of nonlinearities of the two-modefields, we derive a Raman-coupled effective Hamiltonian by a unitary transformation, evaluated perturbatively in couplingconstants. We use the quantum entropy to measure the degree of entanglement in the time development of an effectivetwo-level atom interacting with two-mode nonlinear-coherent states. The results show that the nonlinearity effect yieldsthe superstructure of atomic Rabi oscillations and the effect of the Stark shift changes the quasiperiod of the field entropyevolution and entanglement between the particle and the field. A possible experimental test of a new effect is proposed.     

基于cluster态的信道容量可控的可控量子安全直接通信方案

提出了一种基于五粒子cluster态的信道容量可控的可控量子安全直接通信方案.通信三方利用五粒子cluster态自身的粒子分布情况,结合诱骗光子,对粒子分别做Z基单粒子测量和Bell基测量,便可完成信道的第一次安全性检测.通信控制方Cindy通过对手中的粒子序列随机选用测量基(Z基或者X基)测量来决定信道容量,并通过经典信道公布结果.发送方Alice将要发送的信息以及校检信息用于对手中的粒子序列进行幺正操作编码,并插入诱骗光子后将编码后的粒子序列发给接收方Bob并通过经典信道告知其诱骗光子的位置信息.Bob接收到粒子序列后,按照经典信道Alice发送的信息,结合Cindy公布的信息,剔除诱骗光子后按照一定的规则对手中的两组粒子序列进行Bell基测量,便可解码完成第二次安全性检测以及得到Alice发送的信息.通过对五粒子cluster态的纠缠结构性质进行分析,阐明了五粒子cluster态在该方案中所表现出的特点的物理缘由.结果表明,只需变化测量基的规则和用于编码的粒子,可以将该方案推广成可控双向量子安全直接通信.     

Teleportation of Three-Level Multi-partite Entangled State by a Partial Three-Level Bipartite Entangled State

We present a scheme for probabilistically teleporting an unknown three-level bipartite entangled state by using a partial entangled three-level bipartite state as quantum channel This scheme can be directly generalized to probabilistically teleport an unknown three-level k-particle entangled state by a partial three-level bipartite entangled state. A11 kinds of unitary transformations are given in detail We calculate the successful total probability and the total classical communication cost required for this scheme.     

Controlled Quantum Secure Direct Communication Protocol Based on Huffman Compression Coding

In order to improve the efficiency of quantum secure direct communication, a controlled quantum secure direct communication protocol based on Huffman compression coding is proposed in this paper. The protocol combines classical Huffman coding with quantum communication, Alice performs Huffman compression code and unitary operation on the secret messages and sends them to Bob, and then Bob obtains the corresponding secret messages through decoding operation. In this protocol, communication efficiency can be effectively improved by using Huffman compression coding and sequence generator. As a result, the longer the secret messages, the higher the communication efficiency.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

Probabilistic Remote Preparation of a Four-Particle Entangled W State for the General Case and for All Kinds of the Special Cases

We present a protocol for probabilistic remote preparation of a four-particle entangled W state.The quantum channel is composed of two partial entangled four-particle cluster states.We calculate the total successful probability and total classical communication cost required for the general case and for all kinds of the special cases,respectively.It is shown that for two maximally entangled four-particle cluster states,such a scheme for the general case has the total successful probability of 25%and only consumes the total classical communication of 1 bit,while this scheme for the special cases under certain conditions can possess successful probability of 50%or 100%,the required classical communication will only be 2 bits or 4 bits.Meantime,we give in detail all unitary transformations for the general case and for all kinds of the special cases,respectively.     

A quantum model of collective motion in nuclei and its dequantization

Collective coherent states of Perelomov type are denned by acting with unitary operators from a representation of the symplectic group on the ground state of closed-shell nuclei. A dequantization scheme associates with quantum observables classical ones, and with the state space a phase space and a generalized classical dynamics. Applications to the nuclei ⁴He, ¹⁶O and ⁴⁰Ca are derived from microscopic interactions.