Asymptotic vibrational states of the H-3(+) molecular ion

Vibrational calculations for H-3(+) are performed using an accurate global ab initio potential energy surface. Fourteen bound states close to dissociation are found to have interesting long-range dynamics. These asymptotic vibrational states (AVS) are studied graphically by cuts through their wave functions and by calculating a rotational constant. These AVS, which overlap open system classical trajectories that form half-tori, should lead to an increased density of states near dissociation. Their influence on the infrared near-dissociation spectrum of H-3(+) remains to be determined

Quantum copying can increase the practically available information

While it is known that copying a quantum system does not increase the amount of information obtainable about the originals, it may increase the amount available in practice, when one is restricted to imperfect measurements. We present a detection scheme which using imperfect detectors, and possibly noisy quantum copying machines (that entangle the copies), allows one to extract more information from an incoming signal, than with the imperfect detectors alone. The case of single-photon detection with noisy, inefficient detectors and copiers (single controlled-NOT gates in this case) is investigated in detail. The improvement in distinguishability between a photon and vacuum is found to occur for a wide range of parameters, and to be quite robust to random noise. The properties that a quantum copying device must have to be useful in this scheme are investigated.Comment: 10 pages, 6 figures, accepted PR

Succinct Representations of Dynamic Strings

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing characters of the string to be inserted and deleted. Under the word RAM model with word size $w=\Omega(\lg n)$, we design a succinct representation of dynamic strings using $nH_0 + o(n)\lg\sigma + O(w)$ bits to support rank, select, insert and delete in $O(\frac{\lg n}{\lg\lg n}(\frac{\lg \sigma}{\lg\lg n}+1))$ time. When the alphabet size is small, i.e. when \sigma = O(\polylog (n)), including the case in which the string is a bit vector, these operations are supported in $O(\frac{\lg n}{\lg\lg n})$ time. Our data structures are more efficient than previous results on the same problem, and we have applied them to improve results on the design and construction of space-efficient text indexes

Comment on: "Measuring a Photonic Qubit without Destroying It"

Recently, Pryde et al reported the demonstration of a quantum non-demolition scheme for single-photon polarization states with linear optics and projective measurements [Phys. Rev. Lett. 92, 190402 (2004)]. Here, we argue that their interpretation of the experiment is inconsistent with the fidelity measure they use.Comment: one page, no figure

Entanglement Manipulation and Concentration

We introduce a simple, experimentally realisable, entanglement manipulation protocol for exploring mixed state entanglement. We show that for both non-maximally entangled pure, and mixed polarisation-entangled two qubit states, an increase in the degree of entanglement and purity, which we define as concentration, is achievable.Comment: Accepted as Rapid Communication PR

Entanglement and its Role in Shor's Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not included in the end); v4 is improved following referee comments, expanded explanations and added reference