Authors:Syed M. Assad, Mark Bradshaw, Ping Koy Lam Abstract: International Journal of Quantum Information, Volume 15, Issue 01, February 2017. Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation. Citation: International Journal of Quantum Information PubDate: 2017-02-03T01:12:27Z DOI: 10.1142/S0219749917500095

Authors:Linghang Kong, Elizabeth Crosson Abstract: International Journal of Quantum Information, Ahead of Print. Spike Hamiltonians arise from optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work, we study the efficiency of the adiabatic algorithm for solving the “the Hamming weight with a spike” problem by analyzing the scaling of the spectral gap at the critical point for various sizes of the barrier. Our main result is a rigorous lower bound on the minimum spectral gap for the adiabatic evolution when the bit-symmetric cost function has a thin but polynomially high barrier, which is based on a comparison argument and an improved variational ansatz for the ground state. We also adapt the discrete WKB method for the case of abruptly changing potentials and compare it with the predictions of the spin coherent instanton method which was previously used by Farhi, Goldstone and Gutmann. Finally, our improved ansatz for the ground state leads to a method for predicting the location of avoided crossings in the excited energy states of the thin spike Hamiltonian, and we use a recursion relation to understand the ordering of some of these avoided crossings as a step towards analyzing the previously observed diabatic cascade phenomenon. Citation: International Journal of Quantum Information PubDate: 2017-02-07T10:54:41Z DOI: 10.1142/S0219749917500113

Authors:Cai Zhang, Haozhen Situ, Qiong Huang, Pingle Yang Abstract: International Journal of Quantum Information, Ahead of Print. We propose multi-party quantum summation protocols based on single particles, in which participants are allowed to compute the summation of their inputs without the help of a trusted third party and preserve the privacy of their inputs. Only one participant who generates the source particles needs to perform unitary operations and only single particles are needed in the beginning of the protocols. Citation: International Journal of Quantum Information PubDate: 2017-02-03T09:11:37Z DOI: 10.1142/S0219749917500101

Authors:Ming-Ming Wang, Zhi-Guo Qu, Wei Wang, Jin-Guang Chen Abstract: International Journal of Quantum Information, Ahead of Print. Quantum noise severely affects the security and reliability of quantum communication system. In this paper, we study the effect of quantum noise on quantum multiparty communication protocols. Taking a two-qubit joint remote state preparation (JRSP) scheme as an example, we point out that there are some calculation mistakes in a former JRSP scheme [X.W. Guan, X.B. Chen, L.C. Wang and Y.X. Yang, Int. J. Theor. Phys. 53(4) (2014) 2236.]. The revised output states and fidelities in two types of noise are presented, respectively. More importantly, we present a more general form for describing the effect of noise on multi-qubit system, which is fit for the case where different types of noise act on the system consecutively. The process of the JRSP scheme in two types of noise is discussed, respectively. It is shown that the noisy effect in the general case is much stronger than the former one for the most part. Our study will be helpful for analyzing the effect of quantum noise on quantum multiparty communication system. Citation: International Journal of Quantum Information PubDate: 2017-02-01T09:28:00Z DOI: 10.1142/S0219749917500125

Authors:Jupinder Parmar, Saarim Rahman, Jaskaran Thiara Abstract: International Journal of Quantum Information, Ahead of Print. One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database. Classically, the optimal algorithm is known to have a [math] complexity; however, Grovers algorithm has been found to have an optimal complexity between the lower bound of [math] and the upper bound of [math]. We sought to lower the known upper bound of the OSP. With Farhi et al. MITCTP 2815 (1999), arXiv:quant-ph/9901059], we see that the OSP can be resolved into a translational invariant algorithm to create quantum query algorithm restraints. With these restraints, one can find Laurent polynomials for various [math] — queries — and [math] — database sizes — thus finding larger recursive sets to solve the OSP and effectively reducing the upper bound. These polynomials are found to be convex functions, allowing one to make use of convex optimization to find an improvement on the known bounds. According to Childs et al. [Phys. Rev. A 75 (2007) 032335], semidefinite programming, a subset of convex optimization, can solve the particular problem represented by the constraints. We were able to implement a program abiding to their formulation of a semidefinite program (SDP), leading us to find that it takes an immense amount of storage and time to compute. To combat this setback, we then formulated an approach to improve results of the SDP using matrix sparsity. Through the development of this approach, along with an implementation of a rudimentary solver, we demonstrate how matrix sparsity reduces the amount of time and storage required to compute the SDP — overall ensuring further improvements will likely be made to reach the theorized lower bound. Citation: International Journal of Quantum Information PubDate: 2017-01-13T09:17:34Z DOI: 10.1142/S0219749917500137

Authors:V. G. Bagrov, D. M. Gitman, A. D. Levin, M. S. Meireles Abstract: International Journal of Quantum Information, Ahead of Print. Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field. Citation: International Journal of Quantum Information PubDate: 2017-01-05T06:02:50Z DOI: 10.1142/S021974991750006X

Authors:Divya Taneja, Manish Gupta, Rajesh Narula, Jaskaran Bhullar Abstract: International Journal of Quantum Information, Ahead of Print. Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet. Citation: International Journal of Quantum Information PubDate: 2016-12-29T08:32:51Z DOI: 10.1142/S0219749917500083

Authors:Milad Nanvakenari, Monireh Houshmand Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, a three-party controlled quantum secure direct communication and authentication (QSDCA) protocol is proposed by using four particle cluster states via a quantum one-time pad and local unitary operations. In the present scheme, only under the permission of the controller, the sender and the receiver can implement secure direct communication successfully. But under any circumstances, Charlie cannot obtain the secret message. Eavesdropping detection and identity authentication are achieved with the help of the previously shared reusable base identity strings of users. This protocol is unconditionally secure in both ideal and practical noisy cases. In one transmission, a qubit of each four particle cluster state is used as controller’s permission and the same qubit with another qubit are used to recover two classical bits of information. In the proposed scheme, the efficiency is improved compared with the previous works. Citation: International Journal of Quantum Information PubDate: 2016-12-29T08:32:48Z DOI: 10.1142/S0219749917500022

Authors:Feng Liu Abstract: International Journal of Quantum Information, Ahead of Print. For any [math]-partite state [math], we define its quantum mutual information matrix as an [math][math][math][math][math] matrix whose [math]-entry is given by quantum mutual information [math]. Although each entry of quantum mutual information matrix, like its classical counterpart, is also used to measure bipartite correlations, the similarity ends here: quantum mutual information matrices are not always positive semidefinite even for collections of up to 3-partite states. In this work, we define the genuine n-partite mutual information which can be easily calculated. This definition is symmetric, nonnegative, bounded and more accurate for measuring multipartite states. Citation: International Journal of Quantum Information PubDate: 2016-12-16T07:37:54Z DOI: 10.1142/S0219749917500058

Authors:Kishore Thapliyal, Rishi Dutt Sharma, Anirban Pathak Abstract: International Journal of Quantum Information, Ahead of Print. Two new protocols for quantum binary voting are proposed. One of the proposed protocols is designed using a standard scheme for controlled deterministic secure quantum communication (CDSQC), and the other one is designed using the idea of quantum cryptographic switch, which uses a technique known as permutation of particles. A few possible alternative approaches to accomplish the same task (quantum binary voting) have also been discussed. Security of the proposed protocols is analyzed. Further, the efficiencies of the proposed protocols are computed, and are compared with that of the existing protocols. The comparison has established that the proposed protocols are more efficient than the existing protocols. Citation: International Journal of Quantum Information PubDate: 2016-12-16T07:37:54Z DOI: 10.1142/S0219749917500071

Authors:L. Jebli, B. Benzimoune, M. Daoud Abstract: International Journal of Quantum Information, Ahead of Print. A special emphasis is devoted to the concept of local quantum uncertainty as an indicator of quantum correlations. We study quantum discord for a class of two-qubit states parametrized by two parameters. Quantum discord based on local quantum uncertainty, von Neumann entropy and trace distance (Schatten 1-norm) are explicitly derived and compared. The behavior of quantum correlations, quantified via local quantum uncertainty, under decoherence effects is investigated. We show that the discordlike local quantum uncertainty exhibits the possibility of freezing behavior during its evolution. Citation: International Journal of Quantum Information PubDate: 2016-12-16T07:37:52Z DOI: 10.1142/S0219749917500010

Authors:Hailin Xiao, Ju Ni, Wu Xie, Shan Ouyang Abstract: International Journal of Quantum Information, Ahead of Print. As in classical coding theory, turbo product codes (TPCs) through serially concatenated block codes can achieve approximatively Shannon capacity limit and have low decoding complexity. However, special requirements in the quantum setting severely limit the structures of turbo product codes (QTPCs). To design a good structure for QTPCs, we present a new construction of QTPCs with the interleaved serial concatenation of [math]-type quantum convolutional codes (QCCs). First, [math]-type QCCs are proposed by exploiting the theory of CSS-type quantum stabilizer codes and QCCs, and the description and the analysis of encoder circuit are greatly simplified in the form of Hadamard gates and C-NOT gates. Second, the interleaved coded matrix of QTPCs is derived by quantum permutation SWAP gate definition. Finally, we prove the corresponding relation on the minimum Hamming distance of QTPCs associated with classical TPCs, and describe the state diagram of encoder and decoder of QTPCs that have a highly regular structure and simple design idea. Citation: International Journal of Quantum Information PubDate: 2016-12-16T07:37:52Z DOI: 10.1142/S0219749917500034

Authors:Jin-Zhong Lin Abstract: International Journal of Quantum Information, Ahead of Print. By controlling the parameters of the system, the effective interaction between different atoms is achieved in different cavities. Based on the interaction, scheme to generate three-atom Greenberger–Horne–Zeilinger (GHZ) is proposed in coupled cavities. Spontaneous emission of excited states and decay of cavity modes can be suppressed efficiently. In addition, the scheme is robust against the variation of hopping rate between cavities. Citation: International Journal of Quantum Information PubDate: 2016-12-05T07:17:13Z DOI: 10.1142/S0219749917500046

Authors:Apoorva Patel, Anjani Priyadarsini Abstract: International Journal of Quantum Information, Ahead of Print. Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover’s algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie–Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform. Citation: International Journal of Quantum Information PubDate: 2016-09-14T01:52:34Z DOI: 10.1142/S0219749916500271