QIC Abstracts

 Vol.11 No.7&8 July 1, 2011

Research Articles:

A study of quantum correlations in open quantum systems (pp0541-0562)
Indranil Chakrabarty, Subhashish Banerjee, and Nana Siddharth
In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit (pp0563-0573)
Roman Orus and Tzu-Chieh Wei
In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix product states (MPSs) in the limit of infinite system size. We obtain a lower bound to the GE which collapses to an equality under certain sufficient conditions that are fulfilled by many physical systems, such as those having unbroken space (P) or space-time (PT) inversion symmetry. Our analysis justifies the validity of several derivations carried out in previous works. Second, we derive scaling laws for the GE per site of infinite-size 1D systems with correlation length $\xi \gg 1$. In the case of MPSs, we combine this with the theory of finite-entanglement scaling, allowing to understand the scaling of the GE per site with the MPS bond dimension at conformally invariant quantum critical points.

A new exponential separation between quantum and classical one-way communication complexity (pp0574-0591)
Ashley Montanaro
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously studied Subgroup Membership problem: Alice receives a bit string $x$, Bob receives a permutation matrix $M$, and their task is to determine whether $Mx=x$ or $Mx$ is far from $x$. The proof uses Fourier analysis and an inequality of Kahn, Kalai and Linial.

Optimal deterministic entanglement concentration of polarized photons through direct sum extension (pp0592-0605)
Wen-Dong Li, Wen-Zhao Zhang, Li-Zhen Ma, and Yong-Jian Gu
A scheme for optimal deterministic entanglement concentration is proposed, and its corresponding optical realization based on a cavity-assisted linear optical system is presented. In this scheme, the quantum circuit devised is simpler than that built in [Y. J. Gu, et al. (2006), Phys. Rev. A. 73, 022321], as it requires the minimum ancillary dimensions and the number of unitary operations. Moreover, we show that, by introducing a path-polarization entanglement state based on the direct sum extension method, three elementary controlled phase-flip gates between two photons are sufficient in the design of its optical realization scheme, making it easy to be implemented from the experimental point of view. Meanwhile, the scheme is verified effective to recover highly entangled pairs from mixed states.

Current noise cross correlations and dynamical spin entanglement in coupled quantum dots (pp0606-0614)
Hai-Ffeng Lu, Yong Guo, and Lian-Fu Wei
The authors investigate current noise cross correlations (CCs) through coupled double quantum dots under transport conditions. It is demonstrated that positive CCs relate to either thermal fluctuations at nonzero temperature or quantum tunneling processes at zero temperature. These measurable CCs could service as the sensitive indicators of entanglements between electronic spins in double dots coupled by exchange interactions.

Probabilistic quantum key distribution (pp0615-0637)
Tzonelih Hwang, Chia-Wei Tsai, and Song-Kong Chong
This work presents a new concept in quantum key distribution called the probabilistic quantum key distribution (PQKD) protocol, which is based on the measurement uncertainty in quantum phenomena. It allows two mutually untrusted communicants to negotiate an unpredictable key that has a randomness guaranteed by the laws of quantum mechanics. In contrast to conventional QKD (e.g., BB84) in which one communicant has to trust the other for key distribution or quantum key agreement (QKA) in which the communicants have to artificially contribute subkeys to a negotiating key, PQKD is a natural and simple method for distributing a secure random key. The communicants in the illustrated PQKD take Einstein-Podolsky-Rosen (EPR) pairs as quantum resources and then use entanglement swapping and Bell-measurements to negotiate an unpredictable key.

Different adiabatic quantum optimization algorithms (pp0638-0648)
Vicky Choi

One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001) proposed the adiabatic quantum optimization (AQO), a paradigm that directly attacks NP-hard optimization problems. How powerful is AQO? Early on, van-Dam and Vazirani claimed that AQO failed (i.e. would take exponential time) for a family of 3SAT instances they constructed. More recently, Altshuler, et al. (Proc Natl Acad Sci USA, 107(28): 12446--12450, 2010) claimed that AQO failed also for random instances of the NP-complete Exact Cover problem. In this paper, we make clear that all these negative results are only for a specific AQO algorithm. We do so by demonstrating different AQO algorithms for the same problem for which their arguments no longer hold. Whether AQO fails or succeeds for solving the NP-complete problems (either the worst case or the average case) requires further investigation. Our AQO algorithms for Exact Cover and 3SAT are based on the polynomial reductions to the NP-complete Maximum-weight Independent Set (MIS) problem.

The communication complexity of non-signaling distributions (pp0649-0676)
ulien Degorre, Marc Kaplan, Sophie Laplante, and J\'er\'emie Roland

We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input $x$, Bob gets an input $y$, and their goal is to each produce an output $a,b$ distributed according to some pre-specified joint distribution $p(a,b|x,y)$. Our results apply to any non-signaling distribution, that is, those where Alice's marginal distribution does not depend on Bob's input, and vice versa.~~~By taking a geometric view of the non-signaling distributions, we introduce a simple new technique based on affine combinations of lower-complexity distributions, and we give the first general technique to apply to all these settings, with elementary proofs and very intuitive interpretations. Specifically, we introduce two complexity measures, one which gives lower bounds on classical communication, and one for quantum communication. These measures can be expressed as convex optimization problems.  We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. Despite their apparent simplicity, these lower bounds subsume many known communication complexity lower bound methods, most notably the recent lower bounds of Linial and Shraibman for the special case of Boolean functions.  We show that as in the case of Boolean functions, the gap between the quantum and classical lower bounds is at most linear in the size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequality violations, which was previously known only for the case of distributions with Boolean outcomes and uniform marginals. It also allows us to show that for some distributions, information theoretic methods are necessary to prove strong lower bounds. ~~~ Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution. One consequence of this is a simple proof that any quantum distribution can be approximated with a constant number of bits of communication.

Universality of sudden death of entanglement (pp0677-0694)
Felipe F. Fanchini, Paulo E. M. F. Mendonca, and Reginaldo de J. Napolitano
We present a constructive argument to demonstrate the universality of the sudden death of entanglement in the case of two non-interacting qubits, each of which generically coupled to independent Markovian environments at zero temperature. Conditions for the occurrence of the abrupt disappearance of entanglement are determined and, most importantly, rigourously shown to be \emph{almost} always satisfied: Dynamical models for which the sudden death of entanglement does not occur are seen to form a highly idealized zero-measure subset within the set of all possible quantum dynamics.

Rank-based SLOCC classification for odd $n$ qubits (pp0695-0705)
          Xiangrong Li and Dafa Li
We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect to qubits 1,2, ... n give rise to the classification of the space of odd $n$ qubits into 3^n families.

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