QIC Abstracts

 Vol.13 No.3&4, March 1, 2013

Research Articles:

Sufficient condition on noise correlations for scalable quantum computing (pp0181-0194)
John Preskill

I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise terms acting collectively on $k$ system qubits are sufficiently weak, and decay sufficiently rapidly with increasing $k$ and with increasing spatial separation of the qubits.

Magic-state distillation with the four-qubit code (pp0195-0209)
Adam M. Meier, Bryan Eastin, and Emanuel Knill
The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the $+1$ eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Use of this routine in combination with the $15$-to-$1$ distillation routine described by Bravyi and Kitaev allows for further improvements in overhead.

Optimal class-specific witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry (pp0210-0220)
Christopher Eltschka and Jens Siewert
Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for detecting class-specific entanglement in arbitrary three-qubit states.

Reduction from non-injective hidden shift problem to injective hidden shift problem (pp0221-0230)
Mirmojtaba Gharibi
We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. We generalize the notion of influence and show how it relates to applicability of this tool for doing reductions. In particular, these results can be used to simplify the main results by Gavinsky, Roetteler, and Roland about the hidden shift problem for the Boolean-valued functions and bent functions, and also to generalize their results to non-Boolean domains (thereby answering an open question that they pose).

Gaming the quantum (pp0231-0244)
Faisal Shah Khan and Simon J.D. Phoenix
In the time since the merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of ``quantized games'', and of applying game theory to quantum mechanics, referred to henceforth as ``gaming the quantum'', have become synonymous under the single ill-defined term ``quantum game''. Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multiplayer, non-cooperative game quantum mechanical, is given. Within the context of this description, finding Nash equilibrium in a zero-sum quantum game is exhibited to be equivalent to finding a solution to a simultaneous distance minimization problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of ``equilibrium'' behavior of quantum physical systems such as those utilized in quantum information processing and computation.

Can bipartite classical information resources be activated? (pp0245-0265)
Giuseppe Prettico and Antonio Acin
Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a secret key. Exploiting the analogies between the entanglement and the secret-key agreement scenario, we provide some evidence that the secret-key rate may be a non-additive quantity. In particular, we show that correlations with conjectured bound information become secret-key distillable when combined. Our results constitute a new instance of the subtle relation between the entanglement and secret-key agreement scenario.

Spin squeezing of one-axis twisting model in the presence of phase dephasing (pp0266-0280)
Chen-Guang Ji,Yong-Chun Liu, and Guang-Ri Jin

We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state $|\theta_{0}, \phi_0\rangle$ with the polar angle $\theta_0=\pi/2$. If the dephasing rate $\gamma\ll S^{-1/3}$, where $S$ is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely $\xi^2\propto S^{-2/3}$. While for a moderate dephasing, the achievable squeezing obeys the power rule $S^{-2/5}$, which is slightly worse than the ideal case. When the dephasing rate $\gamma>S^{1/2}$, we show that the squeezing is weak and neglectable.

Cooling distant atoms into steady entanglement via coupled cavities (pp0281-0289)
Li Tuo Shen, Xin Yu Chen, Zhen-Biao Yang, Huai-Zhi Wu, and Shi-Biao Zheng

We propose a scheme for generating steady-state entanglement between two distant atomic qubits in the coupled-cavity system via laser cooling. With suitable choice of the laser frequencies, the target entangled state is the only ground state that is not excited by the lasers due to large detunings. The laser excitations of other ground states, together with dissipative processes, drive the system to the target state which is the unique steady state of the system. Numerical simulation shows that the maximally entangled state with high fidelity can be produced with presently available

Efficient quantum communication under collective noise (pp0290-0323)
Michael Skotiniotis, Wolfgang Dur, and Barbara Kraus
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group $G$, i.e.~with a discrete number, $\lvert G\rvert$, of possible noise operators, perfect transmission at a rate $m/(m+r)$ is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, $r$, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, $m$. For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements $|G|$.

Optical detection of quantum entanglement between two quantum dots mear a metal nanoparticle (pp0324-0333)
Yong He and Ka-Di Zhu
We theoretically study the interaction between two semiconductor quantum dots (SQDs) and a metal nanoparticle\ (MNP) within the quantum description. The plasmon field produced in the MNP excited by the external field can play the platform of F\"{o}rster energy transfer between two SQDs which gives rise to the generation of entangled states. The Fano effect can be shown in the energy absorption spectrum of MNP, which originates from constructive or destructive interference between two competing optical pathways. Since the generated entangled state is in one pathway, the steady-state concurrence of entanglement can be evaluated by the observation of Fano profile. Because the concurrence of two SQDs is determined by both the pump intensity and the energy difference, one can properly choose these two parameters for detecting the non-negligible entanglement. When the pump intensity is very strong, there is no entanglement. The method to observe entanglement with the Fano profile, so, has a limited range of applicability. The optical observation is a novel approach to reveal entanglement. It may be used to optically detect quantum entanglement in many solid-state systems.

Multipartite entanglement in XOR games (pp0334-0360)
Jop Briet, Harry Buhrman, Troy Lee, and Thomas Vidick
We study multipartite entanglement in the context of XOR games. In particular, we study the ratio of the entangled and classical \emph{biases}, which measure the maximum advantage of a quantum or classical strategy over a uniformly random strategy. For the case of two-player XOR games, Tsirelson proved that this ratio is upper bounded by the celebrated Grothendieck constant. In contrast, \PG proved the existence of entangled states that give quantum players an unbounded advantage over classical players in a three-player XOR game. We show that the multipartite entangled states that are most often seen in today's literature can only lead to a bias that is a constant factor larger than the classical bias. These states include GHZ states, any state local-unitarily equivalent to combinations of GHZ and maximally entangled states shared between different subsets of the players (e.g., stabilizer states), as well as generalizations of GHZ states of the form $\sum_i \alpha_i \ket{i}\cdots\ket{i}$ for arbitrary amplitudes $\alpha_i$. Our results have the following surprising consequence: \emph{classical} three-player XOR games do not follow an XOR parallel repetition theorem, even a very weak one. Besides this, we discuss implications of our results for communication complexity and hardness of approximation. Our proofs are based on novel applications of extensions of Grothendieck's inequality, due to Blei and Tonge, and Carne, generalizing Tsirelson's use of Grothendieck's inequality to bound the bias of two-player XOR games.

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