3,575 research outputs found
On cyclic fixed points of spectra
For a finite p-group G and a bounded below G-spectrum X of finite type mod p,
the G-equivariant Segal conjecture for X asserts that the canonical map X^G -->
X^{hG} is a p-adic equivalence. Let C_{p^n} be the cyclic group of order p^n.
We show that if the C_p Segal conjecture holds for a C_{p^n} spectrum X, as
well as for each of its C_{p^e} geometric fixed points for 0 < e < n, then then
C_{p^n} Segal conjecture holds for X. Similar results hold for weaker forms of
the Segal conjecture, asking only that the canonical map induces an equivalence
in sufficiently high degrees, on homotopy groups with suitable finite
coefficients
Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
Universal quantum computation can be achieved by simply performing
single-qubit measurements on a highly entangled resource state, such as cluster
states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been
intensively explored and shown to provide restricted computation. Here, we show
that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb
lattice is a universal resource for measurement-based quantum computation.Comment: 4+2 pages, 4 figures, PRL short version of arXiv:1009.2840, see also
alternative approach by A. Miyake, arXiv:1009.349
The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
Universal quantum computation can be achieved by simply performing
single-qubit measurements on a highly entangled resource state. Resource states
can arise from ground states of carefully designed two-body interacting
Hamiltonians. This opens up an appealing possibility of creating them by
cooling. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states are the ground
states of particularly simple Hamiltonians with high symmetry, and their
potential use in quantum computation gives rise to a new research direction.
Expanding on our prior work [T.-C. Wei, I. Affleck, and R. Raussendorf, Phys.
Rev. Lett. 106, 070501 (2011)], we give detailed analysis to explain why the
spin-3/2 AKLT state on a two-dimensional honeycomb lattice is a universal
resource for measurement-based quantum computation. Along the way, we also
provide an alternative proof that the 1D spin-1 AKLT state can be used to
simulate arbitrary one-qubit unitary gates. Moreover, we connect the quantum
computational universality of 2D random graph states to their percolation
property and show that these states whose graphs are in the supercritical (i.e.
percolated) phase are also universal resources for measurement-based quantum
computation.Comment: 21 pages, 13 figures, long version of Phys. Rev. Lett. 106, 070501
(2011) or arXiv:1102.506
Deterministic and Unambiguous Dense Coding
Optimal dense coding using a partially-entangled pure state of Schmidt rank
and a noiseless quantum channel of dimension is studied both in
the deterministic case where at most messages can be transmitted with
perfect fidelity, and in the unambiguous case where when the protocol succeeds
(probability ) Bob knows for sure that Alice sent message , and when
it fails (probability ) he knows it has failed. Alice is allowed any
single-shot (one use) encoding procedure, and Bob any single-shot measurement.
For a bound is obtained for in terms of the largest
Schmidt coefficient of the entangled state, and is compared with published
results by Mozes et al. For it is shown that is strictly
less than unless is an integer multiple of , in which case
uniform (maximal) entanglement is not needed to achieve the optimal protocol.
The unambiguous case is studied for , assuming for a
set of messages, and a bound is obtained for the average
\lgl1/\tau\rgl. A bound on the average \lgl\tau\rgl requires an additional
assumption of encoding by isometries (unitaries when ) that are
orthogonal for different messages. Both bounds are saturated when is a
constant independent of , by a protocol based on one-shot entanglement
concentration. For it is shown that (at least) messages can
be sent unambiguously. Whether unitary (isometric) encoding suffices for
optimal protocols remains a major unanswered question, both for our work and
for previous studies of dense coding using partially-entangled states,
including noisy (mixed) states.Comment: Short new section VII added. Latex 23 pages, 1 PSTricks figure in
tex
Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
Quantum simulation uses a well-known quantum system to predict the behavior
of another quantum system. Certain limitations in this technique arise,
however, when applied to specific problems, as we demonstrate with a
theoretical and experimental study of an algorithm to find the low-lying
spectrum of a Hamiltonian. While the number of elementary quantum gates does
scale polynomially with the size of the system, it increases inversely to the
desired error bound . Making such simulations robust to decoherence
using fault-tolerance constructs requires an additional factor of
gates. These constraints are illustrated by using a three qubit nuclear
magnetic resonance system to simulate a pairing Hamiltonian, following the
algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure
Types of quantum information
Quantum, in contrast to classical, information theory, allows for different
incompatible types (or species) of information which cannot be combined with
each other. Distinguishing these incompatible types is useful in understanding
the role of the two classical bits in teleportation (or one bit in one-bit
teleportation), for discussing decoherence in information-theoretic terms, and
for giving a proper definition, in quantum terms, of ``classical information.''
Various examples (some updating earlier work) are given of theorems which
relate different incompatible kinds of information, and thus have no
counterparts in classical information theory.Comment: Minor changes so as to agree with published versio
Information theoretic treatment of tripartite systems and quantum channels
A Holevo measure is used to discuss how much information about a given POVM
on system is present in another system , and how this influences the
presence or absence of information about a different POVM on in a third
system . The main goal is to extend information theorems for mutually
unbiased bases or general bases to arbitrary POVMs, and especially to
generalize "all-or-nothing" theorems about information located in tripartite
systems to the case of \emph{partial information}, in the form of quantitative
inequalities. Some of the inequalities can be viewed as entropic uncertainty
relations that apply in the presence of quantum side information, as in recent
work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also
apply to quantum channels: e.g., if \EC accurately transmits certain POVMs,
the complementary channel \FC will necessarily be noisy for certain other
POVMs. While the inequalities are valid for mixed states of tripartite systems,
restricting to pure states leads to the basis-invariance of the difference
between the information about contained in and .Comment: 21 pages. An earlier version of this paper attempted to prove our
main uncertainty relation, Theorem 5, using the achievability of the Holevo
quantity in a coding task, an approach that ultimately failed because it did
not account for locking of classical correlations, e.g. see [DiVincenzo et
al. PRL. 92, 067902 (2004)]. In the latest version, we use a very different
approach to prove Theorem
Recommended from our members
The Communication Patterns Questionnaire-Short Form: A Review and Assessment
The Communication Patterns Questionnaire-Short Form (CPQ-SF) is an 11-item self-assessment of spouses’ perceptions of marital interactions. A cited reference review of the CPQ-SF literature revealed no formal assessment of its psychometric properties and that researchers are imprecise in their use, reporting, and referencing of the assessment. Toward improving the use of the CPQ-SF in research and practice, the factor structure and psychometric properties of this scale were examined with data collected from a diverse sample of married individuals. Three latent constructs were identified: criticize/defend, discuss/avoid, and positive interaction patterns. Support for the original two-factor structure, demand/withdrawal and positive interaction, was also found. Suggestions for a more precise use of the CPQ-SF in research and practice conclude the paper
- …