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Gui Lu Long

Publications and source records attributed to Gui Lu Long.

At least 55 records · Page 3Linked to original sources
arXiv2006

Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in classical computing. All these algorithms are polynomial in the input size.

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arXiv2006

The General Quantum Interference Principle and the Duality Computer

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also proposed thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function

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arXiv2006

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.

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arXiv2006

No-relationship between impossibility of faster-than-light quantum communication and distinction of ensembles with the same density matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related. We argue that: 1) even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or 2) to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.

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arXiv2006

An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen Pairs

An efficient quantum secret sharing scheme is proposed. In this scheme, the particles in an entangled pair group form two particle sequences. One sequence is sent to Bob and the other is sent to Charlie after rearranging the particle orders. Bob and Charlie make coding unitary operations and send the particles back. Alice makes Bell-basis measurement to read their coding operations.

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arXiv2006

Proof of Security of a High-Capacity Quantum Key Distribution Protocol

We prove the security of a high-capacity quantum key distribution protocol over noisy channels. By using entanglement purification protocol, we construct a modified version of the protocol in which we separate it into two consecutive stages. We prove their securities respectively and hence the security of the whole protocol.

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arXiv2005

Comment on quant-ph/0506105: The modified Grover algorithm cannot speedup unsorted database search

In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true, it would represent a major fundamental breakthrough in computer science, mathematics, quantum information and other related branches of sciences. However the algorithm is not valid. We will explain it in this brief comment.

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arXiv2005

Bidirectional quantum secret sharing and secret splitting with polarized single photons

In this Letter, we present quantum secret sharing and secret splitting protocols with single photons running forth and back between the participating parties. The protocol has a high intrinsic efficiency, namely all photons except those chosen for eavesdropping check could be used for sharing secret. The participants need not to announce the measuring bases at most of the time and this reduces the classical information exchanged largely.

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arXiv2005

Simulation of a Heisenberg XY- chain and realization of a perfect state transfer algorithm using liquid nuclear magnetic resonance

The three- spin chain with Heisenberg XY- interaction is simulated in a three- qubit nuclear magnetic resonance (NMR) quantum computer. The evolution caused by the XY- interaction is decomposed into a series of single- spin rotations and the $J$- coupling evolutions between the neighboring spins. The perfect state transfer (PST) algorithm proposed by M. Christandl et al [Phys. Rev. Lett, 92, 187902(2004)] is realized in the XY- chain.

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arXiv2004

Coherence Control of Adiabatic Decoherence in a Three-level Atom with Lambda Configuration

In this paper, we study the suppression of adiabatic decoherence in a three-level atom with $Λ$ configuration using bang-bang control technique. We have given the decoupling bang-bang operation group, and programmed a sequence of periodic radio frequency twinborn pulses to realize the control process. Moreover, we have studied the process with non-ideal situation and established the condition for efficient suppression of adiabatic decoherence.

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arXiv2004

Modularization of multi-qubit controlled phase gate and its NMR implementation

Quantum circuit network is a set of circuits that implements a certain computation task. Being at the center of the quantum circuit network, the multi-qubit controlled phase shift is one of the most important quantum gates. In this paper, we apply the method of modular structuring in classical computer architecture to quantum computer and give a recursive realization of the multi-qubit phase gate. This realization of the controlled phase shift gate is convenient in realizing certain quantum algorithms. We have experimentally implemented this modularized multi-qubit controlled phase gate in a three qubit nuclear magnetic resonance quantum system. The network is demonstrated experimentally using line selective pulses in nuclear magnetic resonance technique. The procedure has the advantage of being simple and easy to implement.

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arXiv2004

Quantum privacy amplification for quantum secure direct communication

Using quantum mechanics, secure direct communication between distant parties can be performed. Over a noisy quantum channel, quantum privacy amplification is a necessary step to ensure the security of the message. In this paper, we present a quantum privacy amplification scheme for quantum secure direct communication using single photons. The quantum privacy amplification procedure contains two control-not gates and a Hadamard gate. After the unitary gate operations, a measurement is performed and one photon is retained. The retained photon carries the state information of the discarded photon, and hence reduces the information leakage. The procedure can be performed recursively so that the information leakage can be reduced to any arbitrarily low level.

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arXiv2004

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.

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arXiv2004

Efficient Multi-Party Quantum Secret Sharing Schemes

In this work, we generalize the quantum secret sharing scheme of Hillary, Bužek and Berthiaume[Phys. Rev. A59, 1829(1999)] into arbitrary multi-parties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bužek-Berthiaume quantum secret sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum secret sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis Quantum secret sharing scheme is developed from the Lo-Chau-Ardehali technique[H. K. Lo, H. F. Chau and M. Ardehali, quant-ph/0011056] where all the participants choose their measuring-basis asymmetrically, and the measuring-basis-encrypted Quantum secret sharing scheme is developed from the Hwang-Koh-Han technique [W. Y. Hwang, I. G. Koh and Y. D. Han, Phys. Lett. A244, 489 (1998)] where all participants choose their measuring-basis according to a control key. Both schemes are asymptotically 100% in efficiency, hence nearly all the GHZ-states in a quantum secret sharing process are used to generate shared secret information.

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