Vol.12 No.7&8, July 1, 2012

Research Articles:

Non-demolition dispersive measurement of a superconducting qubit with a microstrip SQUID amplifier (pp0541-0552)
          G.P. Berman, D.I. Kamenev, D. Kinion, and V.I. Tsifrinovich
We have studied the possibility of a single-shot non-demolition measurement of a superconducting qubit using a microstrip SQUID amplifier (MSA). The Johnson noise generated by all resistors in the MSA is taken into consideration. We show that a single-shot non-demolition measurement is possible with six photons in the measurement resonator.

Improving quantum clocks via semidefinite programming (pp0553-0574)
          Michael Mullan and Emanuel Knill
The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations or the probe times. We consider arbitrary prior frequency knowledge and compare clocks with varying numbers of ions and queries interlaced with unitary control. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.

Quantum predictive learning and communication complexity with single input (pp0575-0588)
          Dmitry Gavinsky
We define a new model of quantum learning that we call \e{Predictive Quantum (\pq)}. This is a quantum analogue of \pac, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational concept class that is \e{efficiently learnable} in \pq, while in \e{any} ``reasonable'' classical model exponential amount of training data would be required. This is the first unconditional separation between quantum and classical learning. We show that our separation is the best possible in several ways; in particular, there is no analogous result for a functional class, as well as for several weaker versions of quantum learning. In order to demonstrate tightness of our separation we consider a special case of one-way communication that we call \e{single-input mode}, where Bob receives no input. Somewhat surprisingly, this setting becomes nontrivial when relational communication tasks are considered. In particular, any problem with two-sided input can be transformed into a single-input relational problem of equal \e{classical} one-way cost. We show that the situation is different in the \e{quantum} case, where the same transformation can make the communication complexity exponentially larger. This happens if and only if the original problem has exponential gap between quantum and classical one-way communication costs. We believe that these auxiliary results might be of independent interest.

On QMA protocols with two short quantum proofs (pp0589-0600)
          Francois Le Gall, Shota Nakagawa, and Harumichi Nishimura
This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is $\Omega(\frac{1}{n\polylog{n}})$.  This improves the best completeness/soundness gaps known for NP-complete problems in this setting.

Fast iSWAP gate using two $Q$ switches (pp0601-0608)
          Jie Song, Yan Xia, Xiu-Dong Sun, and He-Shan Song
An effective approach to the construction of iSWAP gate has been proposed. Working with three atoms inside three coupled cavities, we analyze the transport and the confinement of a single photon along two different directions. It is shown that two $Q$ switches can be built by tuning the transition energy of each atom. Applying a classical field, we can implement high-speed gate operation between photon and atom. In addition, the influence of decoherence on the gate fidelity is also discussed.

On the existence of loss-tolerant quantum oblivious transfer protocols (pp0609-0619)
          Jamie Sikora
Oblivious transfer is the cryptographic primitive where Alice sends one of two bits to Bob but is oblivious to the bit received. Using quantum communication, we can build oblivious transfer protocols with security provably better than any protocol built using classical communication. However, with imperfect apparatus, one needs to consider other attacks. In this paper, we present an oblivious transfer protocol which is impervious to lost messages.

An optical scheme for quantum multi-service network (pp0620-0629)
          Fabio Alencar Mendonca, Daniel Barbosa de Brito, and Rubens Viana Ramos
Several quantum protocols for data security having been proposed and, in general, they have different optical implementations. However, for the implementation of quantum protocols in optical networks, it is highly advantageous if the same optical setup can be used for running different quantum communication protocols. In this direction, here we show an optical scheme that can be used for quantum key distribution (QKD), quantum secure direct communication (QSDC) and quantum secret sharing (QSS). Additionally, it is naturally resistant to the attack based on single-photon detector blinding. At last, we show a proof-of-principle experiment in 1 km optical fiber link that shows the feasibility of the proposed scheme.

The security of SARG04 protocol in plug and play QKD system with an untrusted source (pp0630-0647)
          Bingjie Xu, Xiang Peng, and Hong Guo
The SARG04 protocol is one of the most frequently used protocol in commercial plug-and-play quantum key distribution (QKD) system, where an eavesdropper can completely control or change the photon number statistics of the QKD source. To ensure the security of SARG04 protocol in plug-and-play QKD system with an unknown and untrusted source, the bounds of a few statistical parameters of the source need to be monitored. An active or a passive source monitor schemes are proposed to verify these parameters. Furthermore, the practical issues due to statistical fluctuation and detection noise in the source monitoring process are quantitatively analyzed. Our simulation results show that the passive scheme can be efficiently applied to plug-and-play system with SARG04 protocol.

How to counteract systematic errors in quantum state transfer (pp0648-0660)
          Chiara Marletto, Alastair Kay, and Artur Ekert
In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of the chain, are small compared to the length of the chain, growing linearly with the size of the error. We also describe how these errors can be identified, again by only acting on the encoding and decoding regions.

Finding hidden Borel subgroups of the general linear group (pp0661-0669)
          Gabor Ivanyos
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The complexity of the algorithm is polynomial when size of the base field is not much smaller than the degree.

The quantum query complexity of AC0 (pp0670-0676)
          Paul Beame and Widad Machmouchi
We show that any quantum algorithm deciding whether an input function $f$ from $[n]$ to $[n]$ is 2-to-1 or almost 2-to-1 requires $\Theta(n)$ queries to $f$. The same lower bound holds for determining whether or not a function $f$ from $[2n-2]$ to $[n]$ is surjective. These results yield a nearly linear $\Omega(n/\log n)$ lower bound on the quantum query complexity of $\cl{AC}^0$. The best previous lower bound known for any $\cl{AC^0}$ function was the $\Omega ((n/\log n)^{2/3})$ bound given by Aaronson and Shi's $\Omega(n^{2/3})$ lower bound for the element distinctness problem.
Quantum discord of a three-qubit W-class state in noisy environments (pp0677-0692)
          Hui Guo, Jin-Ming Liu, Cheng-Jie Zhang, and C. H. Oh
We study the dynamics of the pairwise quantum discord (QD), classical correlation (CC), and entanglement of formation (EOF) for the three-qubit W-class state |W>_{123}=\frac 12(|100>_{123}+|010>_{123}+\sqrt{2}|001>_{123}) under the influence of various Markovian noises by analytically solving the master equation in the Lindblad form. Through numerical analysis, we find that EOF decreases asymptotically to zero with time for the dephasing noise, but it undergoes sudden death for the bit-flip noise, the isotropic noise, as well as the dissipative and noisy environments. Moreover, QD decays to zero in an asymptotical way for all the noises we investigated. Thus, when the W-class state |W>_{123} is subject to the above Markovian noises, QD is more robust than EOF against decoherence excluding the phase-flip noise, implying that QD is more useful than entanglement to characterize the quantum correlation. We also find a remarkable character for the CC in the presence of the phase-flip noise, i.e., CC displays the behavior of sudden transition and then keeps constant permanently, but the corresponding QD just exhibits a very small sudden change. Furthermore, we verify the monogamic relation between the pairwise QD and EOF of the W-class state.

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