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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)
Julien 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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