5,737 research outputs found
Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
We prove a concise factor-of-2 estimate for the failure rate of optimally
distinguishing an arbitrary ensemble of mixed quantum states, generalizing work
of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis,
MIT, 1979]. A modification to the minimal principle of Cocha and Poor
[Proceedings of the 6th International Conference on Quantum Communication,
Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a
suboptimal measurement which has an error rate within a factor of 2 of the
optimal by construction. This measurement is quadratically weighted and has
appeared as the first iterate of a sequence of measurements proposed by Jezek
et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good
measurement, it coincides with Holevo's asymptotically optimal measurement in
the case of nonequiprobable pure states. A quadratically weighted version of
the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is
proven. Bounds on the distinguishability of syndromes in the sense of
Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a
corollary. An appendix relates our bounds to the trace-Jensen inequality.Comment: It was not realized at the time of publication that the lower bound
of Theorem 10 has a simple generalization using matrix monotonicity (See [J.
Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial
variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans.
Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the autho
How to hide a secret direction
We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur
Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
Decoherence-free subspaces (DFSs) shield quantum information from errors
induced by the interaction with an uncontrollable environment. Here we study a
model of correlated errors forming an Abelian subgroup (stabilizer) of the
Pauli group (the group of tensor products of Pauli matrices). Unlike previous
studies of DFSs, this type of errors does not involve any spatial symmetry
assumptions on the system-environment interaction. We solve the problem of
universal, fault-tolerant quantum computation on the associated class of DFSs.Comment: 22 pages, 4 figures. Sequel to quant-ph/990806
Biological evidence supports an early and complex emergence of the Isthmus of Panama.
The linking of North and South America by the Isthmus of Panama had major impacts on global climate, oceanic and atmospheric currents, and biodiversity, yet the timing of this critical event remains contentious. The Isthmus is traditionally understood to have fully closed by ca. 3.5 million years ago (Ma), and this date has been used as a benchmark for oceanographic, climatic, and evolutionary research, but recent evidence suggests a more complex geological formation. Here, we analyze both molecular and fossil data to evaluate the tempo of biotic exchange across the Americas in light of geological evidence. We demonstrate significant waves of dispersal of terrestrial organisms at approximately ca. 20 and 6 Ma and corresponding events separating marine organisms in the Atlantic and Pacific oceans at ca. 23 and 7 Ma. The direction of dispersal and their rates were symmetrical until the last ca. 6 Ma, when northern migration of South American lineages increased significantly. Variability among taxa in their timing of dispersal or vicariance across the Isthmus is not explained by the ecological factors tested in these analyses, including biome type, dispersal ability, and elevation preference. Migration was therefore not generally regulated by intrinsic traits but more likely reflects the presence of emergent terrain several millions of years earlier than commonly assumed. These results indicate that the dramatic biotic turnover associated with the Great American Biotic Interchange was a long and complex process that began as early as the Oligocene-Miocene transition
Exchange Interaction Between Three and Four Coupled Quantum Dots: Theory and Applications to Quantum Computing
Several prominent proposals have suggested that spins of localized electrons
could serve as quantum computer qubits. The exchange interaction has been
invoked as a means of implementing two qubit gates. In this paper, we analyze
the strength and form of the exchange interaction under relevant conditions. We
find that, when several spins are engaged in mutual interactions, the
quantitative strengths or even qualitative forms of the interactions can
change. It is shown that the changes can be dramatic within a Heitler-London
model. Hund-Mulliken calculations are also presented, and support the
qualititative conclusions from the Heitler-London model. The effects need to be
considered in spin-based quantum computer designs, either as a source of gate
error to be overcome or a new interaction to be exploited.Comment: 16 pages, 16 figures. v3: Added Hund-Mulliken calculations in 3-dots
case. A few small corrections. This version submitted to PR
On SIC-POVMs in Prime Dimensions
The generalized Pauli group and its normalizer, the Clifford group, have a
rich mathematical structure which is relevant to the problem of constructing
symmetric informationally complete POVMs (SIC-POVMs). To date, almost every
known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the
Clifford group. I show that every canonical unitary in prime dimensions p > 3
lies in the same conjugacy class of the Clifford group and give a class
representative for all such dimensions. It follows that if even one such
SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them
are (for a given such dimension). I also conjecture that in all dimensions d,
the number of conjugacy classes is bounded above by 3 and depends only on d mod
9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous
work. Ref to a proof of the main conjecture also adde
Interactions of Bacillus Mojavensis and Fusarium Verticillioides With a Benzoxazolinone (Boa) and Its Transformation Product, Apo
En:Journal of Chemical Ecology (2007, vol. 33, n. 10, p. 1885-1897)The benzoxazolinones, specifically benzoxazolin-2(3H)-one (BOA), are important transformation products of the benzoxazinones that can serve as allelochemicals providing resistance to maize from pathogenic bacteria, fungi, and insects. However, maize pathogens such as Fusarium verticillioides are capable of detoxifying the benzoxazolinones to 2-aminophenol (AP), which is converted to the less toxic N-(2-hydroxyphenyl) malonamic acid (HPMA) and 2-acetamidophenol (HPAA). As biocontrol strategies that utilize a species of endophytic bacterium, Bacillus mojavensis, are considered efficacious as a control of this Fusarium species, the in vitro transformation and effects of BOA on growth of this bacterium was examined relative to its interaction with strains of F. verticillioides. The results showed that a red pigment was produced and accumulated only on BOA-amended media when wild type and the progeny of genetic crosses of F. verticillioides are cultured in the presence of the bacterium. The pigment was identified as 2-amino-3H-phenoxazin-3-one (APO), which is a stable product. The results indicate that the bacterium interacts with the fungus preventing the usual transformation of AP to the nontoxic HPMA, resulting in the accumulation of higher amounts of APO than when the fungus is cultured alone. APO is highly toxic to F. verticillioides and other organisms. Thus, an enhanced biocontrol is suggested by this in vitro study.
=580 $aEn:Journal of Chemical Ecolog
The Communication Cost of Simulating Bell Correlations
What classical resources are required to simulate quantum correlations? For
the simplest and most important case of local projective measurements on an
entangled Bell pair state, we show that exact simulation is possible using
local hidden variables augmented by just one bit of classical communication.
Certain quantum teleportation experiments, which teleport a single qubit,
therefore admit a local hidden variables model.Comment: 4 pages, 2 figures; reference adde
Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
A general scheme to perform universal quantum computation within
decoherence-free subspaces (DFSs) of a system's Hilbert space is presented.
This scheme leads to the first fault-tolerant realization of universal quantum
computation on DFSs with the properties that (i) only one- and two-qubit
interactions are required, and (ii) the system remains within the DFS
throughout the entire implementation of a quantum gate. We show explicitly how
to perform universal computation on clusters of the four-qubit DFS encoding one
logical qubit each under "collective decoherence" (qubit-permutation-invariant
system-bath coupling). Our results have immediate relevance to a number of
solid-state quantum computer implementations, in particular those in which
quantum logic is implemented through exchange interactions, such as the
recently proposed spin-spin coupled GaAs quantum dot arrays and the Si:P
nuclear spin arrays.Comment: 5 pages, no figures. Many small changes and clarifications. Expanded
discussion of relevance to solid-state implementations. This version to
appear in Phys. Rev. Let
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