Li Jing, Yi-Nan Wang, Han-Duo Shi, Liang-Zhu Mu, Heng Fan
We study the minimal input sets which can determine completely the universal and the phase-covariant quantum cloning machines. We find that the universal quantum cloning machine, which can copy arbitrary input qubit equally well, however can be determined completely by only four input states located at the four vertices of a tetrahedron. The phase-covariant quantum cloning machine, which can copy all qubits located on the equator of the Bloch sphere, can be determined by three equatorial qubits with equal angular distance. These results sharpen further the well-known results that BB84 states and six-states used in quantum cryptography can determine completely the phase-covariant and universal quantum cloning machines. This concludes the study of the power of universal and phase-covariant quantum cloning, i.e., from minimal input sets necessarily to full input sets by definition. This can simplify dramatically the testing of whether the quantum clone machines are successful or not, we only need to check that the minimal input sets can be cloned optimally.
Yu-xin Liu, Liang-zhu Mu
With the energy surface of the nucleus in U(5) symmetry being analyzed in the framework of thermodynamics, the vibration and rotation phase diagram in terms of the angular momentum and deformation parameter is given. Together with examining the energy spectrum, we propose a theoretical approach to describe the vibrational to axially rotational phase transition along the yrast line. By analyzing the available experimental data we show that the vibrational to rotational shape phase transition along the yrast line takes place in many nuclei.
Ding Zhong, Jian Wang, Ning Dai, Liang-Zhu Mu, Heng Fan
Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The inevitable decoherence is harmful to the realization of those quantum gates. Here, we investigate the performance of the quantum gates exposed to different type of noises. We find that some errors may not influence the success of the quantum gates, in contrast, some others may destroy their realization. We show that there is a controlling pattern that can protect quantum gates from certain types of noises and thus can improve the success probability of the gates implementation.
Yong-Liang Zhang, Yi-Nan Wang, Xiang-Ru Xiao, Li Jing, Liang-Zhu Mu, V. E. Korepin, Heng Fan
We investigate the schemes of quantum network teleportation for quantum information distribution and concentration which are essential in quantum cloud computation and quantum internet. In those schemes, the cloud can send simultaneously identical unknown quantum states to clients located in different places by a network like teleportation with a prior shared multipartite entangled state resource. The cloud first perform the quantum operation, each client can recover their quantum state locally by using the classical information announced by the cloud about the measurement result. The number of clients can be beyond the number of identical quantum states intentionally being sent, this quantum network teleportation can make sure that the retrieved quantum state is optimal. Furthermore, we present a scheme to realize its reverse process, which concentrates the states from the clients to reconstruct the original state of the cloud. These schemes facilitate the quantum information distribution and concentration in quantum networks in the framework of quantum cloud computation. Potential applications in time synchronization are discussed.
Shang Liu, Liang-Zhu Mu, Heng Fan
Oct 20, 2014·quant-ph·PDF We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can be proven in a unified method and easy to calculate. Our results recover the well known entropic uncertainty relations for two observables, which show the uncertainties about the outcomes of two incompatible measurements. Those uncertainty relations are applicable in both foundations of quantum theory and the security of many quantum cryptographic protocols.
He-Ming Wang, Heng-Yun Zhou, Liang-Zhu Mu, Heng Fan
Dec 17, 2013·quant-ph·PDF We formulate a series of non-trivial equalities which are satisfied by all no-signaling correlations, meaning that no faster-than-light communication is allowed with the resource of these correlations. All quantum and classical correlations satisfy these equalities since they are no-signaling. By applying these equalities, we provide a general framework for solving the multipartite "guess your neighbor's input" (GYNI) game, which is naturally no-signaling but shows conversely that general no-signaling correlations are actually more non-local than those allowed by quantum mechanics. We confirm the validity of our method for number of players from 3 up to 19, thus providing convincing evidence that it works for the general case. In addition, we solve analytically the tripartite GYNI and obtain a computable measure of supra-quantum correlations. This result simplifies the defined optimization procedure to an analytic formula, thus characterizing explicitly the boundary between quantum and supra-quantum correlations. In addition, we show that the gap between quantum and no-signaling boundaries containing supra-quantum correlations can be closed by local orthogonality conditions in the tripartite case. Our results provide a computable classification of no-signaling correlations.
Hong Qiao, Zheng-Hang Sun, Feng-Xiao Sun, Liang-Zhu Mu, Qiongyi He, Heng Fan
Aug 31, 2018·quant-ph·PDF We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which can not show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.
Yi-Nan Wang, Han-Duo Shi, Zhao-Xi Xiong, Li Jing, Xi-Jun Ren, Liang-Zhu Mu, Heng Fan
Apr 20, 2011·quant-ph·PDF We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection which reduces dramatically the difficulties for implementation. Also it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.
Heng Fan, Yi-Nan Wang, Li Jing, Jie-Dong Yue, Han-Duo Shi, Yong-Liang Zhang, Liang-Zhu Mu
Jan 14, 2013·quant-ph·PDF No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.
Xi Chen, He-Ming Wang, Liang-Zhu Mu, Heng Fan
May 15, 2014·quant-ph·PDF Quantum state can be teleported to a remote site by only local measurement and classical communication if the prior Einstein-Podolsky-Rosen quantum channel is available between the sender and the receiver. Those quantum channels shared by multiple nodes can constitute a quantum network. Yet, studies on the efficiency of quantum communication between nodes of quantum networks remain limited, which differs from classical case in that the quantum channel will be consumed if teleportation is performed. Here, we introduce the exclusive quantum channels (EQC) as the measure of efficiency of quantum information transmission. It quantifies the amount of quantum information which can be teleported between nodes in a quantum network. We show that different types of EQC are local quantities with effective circles. Significantly, capacity of quantum communication of quantum networks quantified by EQC is independent of distance for the communicating nodes. Thus, the quantum network can be dealt as the isotropic medium where quantum communication is no-decaying. EQC are studied by both analytical and numerical methods. The EQC can be enhanced by transformations of lattices of quantum network via entanglement swapping. Our result opens the avenue in studying the quantum communication of the quantum networks.
Yong-Liang Zhang, Yu-Ran Zhang, Liang-Zhu Mu, Heng Fan
Mar 14, 2013·quant-ph·PDF We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $σ$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $σ$; otherwise the difference is beyond $σ$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $σ\simπ/{(ω(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.
Bing-Tian Ye, Zhao-Yu Han, Liang-Zhu Mu, Heng Fan
We study the entanglement in momentum space of the ground state of a disordered one-dimensional fermion lattice model with attractive interaction. We observe two components in the entanglement spectrum, one of which is related to paired-fermion entanglement and contributes to the long-range correlation in position space. The vanishing point of it indicates the localization phenomenon in the ground state of this model. Additionally, by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and fnd that this phase transition is not infuenced by the disorder. Our result show key characteristics in entanglement for different phases in the system, and provide a novel perspective to understand localization phenomena.
Liang-zhu Mu, Yu-xin Liu
The shape phase structure and its transition of the nucleus in the transitional region between the U(5) and SU(3) symmetries is restudied within the framework of coherent-state theory with angular momentum projection in IBM-1. The certain angular momentum (or rotation-driven) effect on the nuclear shape is discussed. A coexistence of prolate and oblate shapes is found for the ground states of the transitional nuclei. A phase diagram in terms of the deformation parameter and angular momentum is given.
Yi-Nan Wang, Han-Duo Shi, Li Jing, Zhao-Xi Xiong, Jin Lei, Liang-Zhu Mu, Heng Fan
May 26, 2011·quant-ph·PDF We raise a general question of quantum information theory whether the quantum phase information can be compressed and retrieved. A general qubit contains both amplitude and phase information, while an equatorial qubit contains only a phase information. We study whether it is possible to compress the phase information of n equatorial qubits into m general qubits with m being less than n, and still those information can be retrieved perfectly. We prove that this process is not allowed by quantum mechanics.
Wen Wang, Xu Jiang, Liang-zhu Mu, Heng Fan
Jul 20, 2017·quant-ph·PDF We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This algorithm is an application of the quantum algorithms for the hidden subgroup problems, the same as Shor factoring algorithm. Explicit quantum circuits realized by quantum gates for this quantum algorithm are provided. We also give a computer simulation of this quantum algorithm and present the expected outcomes for the corresponding quantum circuit.
Zichen Yang, Ze-Yang Fan, Liang-Zhu Mu, Heng Fan
We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number of users is generated at each port by ensemble of known quantum states with assistance of classical information of measurement outcomes by broadcasting. The obtained quantum state for each user is optimal in the sense that the fidelity universally achieves the upper bound. We present the universal quantum state distribution by providing physical realizable measurement bases in the cloud as well as the reconstruction method for each user. The quantum state reconstruction scheme works for arbitrary many identical pure input states in general dimensional system.
Bing-Tian Ye, Liang-Zhu Mu, Heng Fan
We investigate the entanglement spectrum of the ground state of Su-Schrieffer-Heeger-Hubbard model. The topological phases of the model can be identified by degeneracy of the largest eigenvalues of entanglement spectrum. The study of the periodic boundary condition is enough to obtain the phase diagram of the model, without the consideration of the open boundary condition case. Physical interpretation about the bulk-edge correspondence in the entanglement spectrum is presented. The method of the entanglement spectrum can be applicable in studying other topological phases of matter.
Qian-Tan Hong, Zi-Yong Ge, Wen Wang, Hai-Feng Lang, Zheng-An Wang, Yi Peng, Jin-Jun Chen, Li-Hang Ren, Yu Zeng, Liang-Zhu Mu, Heng Fan
Jun 18, 2018·quant-ph·PDF A medium-scale quantum computer with full universal quantum computing capability is necessary for various practical aims and testing applications. Here we report a 34-qubit quantum virtual machine (QtVM) based on a medium server. Our QtVM can run quantum assembly language with graphic interfaces. The QtVM is implemented with single qubit rotation gate, single to multiple controlled NOT gates to realize the universal quantum computation. Remarkably, it can realize a series of basic functions, such as, the "if" conditional programming language based on single-shot projective measurement results, "for" iteration programming language, build in arithmetic calculation. The measurement can be single-shot and arbitrary number of multi-shot types. In addition, there is in principle no limitation on number of logic gates implemented for quantum computation. By using QtVM, we demonstrate the simulation of dynamical quantum phase transition of transverse field Ising model by quantum circuits, where 34 qubits with one million gates are realized. We also show the realization of programmable Shor algorithm for factoring 15 and 35.
Yong-Liang Zhang, Huan Wang, Li Jing, Liang-Zhu Mu, Heng Fan
Jan 21, 2014·quant-ph·PDF We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
Han-Duo Shi, Yi-Nan Wang, Li Jing, Ru-Quan Wang, Liang-Zhu Mu, Heng Fan
May 16, 2012·quant-ph·PDF This paper is withdrawn. We study the quantum key distribution (QKD) protocol based on a quantum retrodiction protocol, namely the so-called mean king problem. The security is analyzed by considering the eavesdropping on both the preparation of the entangled pair and the transmission of the quantum state. This QKD protocol can generate efficiently a bit of raw key in every single run. We find that, for qubit system, it is more secure than the QKD Bennett-Brassard 1984 protocol and the six-state protocol. This QKD protocol works also for higher dimensional system.