6,432 research outputs found
Testing product states, quantum Merlin-Arthur games and tensor optimisation
We give a test that can distinguish efficiently between product states of n
quantum systems and states which are far from product. If applied to a state
psi whose maximum overlap with a product state is 1-epsilon, the test passes
with probability 1-Theta(epsilon), regardless of n or the local dimensions of
the individual systems. The test uses two copies of psi. We prove correctness
of this test as a special case of a more general result regarding stability of
maximum output purity of the depolarising channel. A key application of the
test is to quantum Merlin-Arthur games with multiple Merlins, where we obtain
several structural results that had been previously conjectured, including the
fact that efficient soundness amplification is possible and that two Merlins
can simulate many Merlins: QMA(k)=QMA(2) for k>=2. Building on a previous
result of Aaronson et al, this implies that there is an efficient quantum
algorithm to verify 3-SAT with constant soundness, given two unentangled proofs
of O(sqrt(n) polylog(n)) qubits. We also show how QMA(2) with log-sized proofs
is equivalent to a large number of problems, some related to quantum
information (such as testing separability of mixed states) as well as problems
without any apparent connection to quantum mechanics (such as computing
injective tensor norms of 3-index tensors). As a consequence, we obtain many
hardness-of-approximation results, as well as potential algorithmic
applications of methods for approximating QMA(2) acceptance probabilities.
Finally, our test can also be used to construct an efficient test for
determining whether a unitary operator is a tensor product, which is a
generalisation of classical linearity testing.Comment: 44 pages, 1 figure, 7 appendices; v6: added references, rearranged
sections, added discussion of connections to classical CS. Final version to
appear in J of the AC
On Validating Closed-Loop Behaviour from Noisy Frequency-Response Measurements
It is shown how noisy closed-loop frequency-response measurements can be used to obtain pointwise in frequency bounds on the possible difference between the actual closed-loop system and the closed-loop comprising a nominal model of the plant and the stabilising controller. To this end, Vinnicombe's gap metric framework for robustness analysis plays a central role. Indeed, an optimisation problem and corresponding algorithm are proposed for estimating the chordal distance between the frequency responses of the nominal plant model and a plant that is consistent with the closed-loop data and a priori information, when projected onto the Riemann sphere
An evaluation of biotic ligand models predicting acute copper toxicity to Daphnia magna in wastewater effluent
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2010 SETAC.The toxicity of Cu to Daphnia magna was investigated in a series of 48-h immobilization assays in effluents from four wastewater treatment works. The assay results were compared with median effective concentration (EC50) forecasts produced by the HydroQual biotic ligand model (BLM), the refined D. magna BLM, and a modified BLM that was constructed by integrating the refined D. magna biotic ligand characterization with the Windermere humic aqueous model (WHAM) VI geochemical speciation model, which also accommodated additional effluent characteristics as model inputs. The results demonstrated that all the BLMs were capable of predicting toxicity by within a factor of two, and that the modified BLM produced the most accurate toxicity forecasts. The refined D. magna BLM offered the most robust assessment of toxicity in that it was not reliant on the inclusion of effluent characteristics or optimization of the dissolved organic carbon active fraction to produce forecasts that were accurate by within a factor of two. The results also suggested that the biotic ligand stability constant for Na may be a poor approximation of the mechanisms governing the influence of Na where concentrations exceed the range within which the biotic ligand stability constant value had been determined. These findings support the use of BLMs for the establishment of site-specific water quality standards in waters that contain a substantial amount of wastewater effluent, but reinforces the need for regulators to scrutinize the composition of models, their thermodynamic and biotic ligand parameters, and the limitations of those parameters.EPSRC and Severn Trent Water
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