Might Carbon-Atmosphere White Dwarfs Harbour a New Type of Pulsating Star?

In the light of the recent and unexpected discovery of a brand new type of white dwarfs, those with carbon-dominated atmospheres, we examine the asteroseismological potential of such stars. The motivation behind this is based on the observation that past models of carbon-atmosphere white dwarfs have partially ionized outer layers that bear strong resemblance with those responsible for mode excitation in models of pulsating DB (helium-atmosphere) and pulsating DA (hydrogen-atmosphere) white dwarfs. Our exciting main result is that, given the right location in parameter space, some carbon-atmosphere white dwarfs are predicted to show pulsational instability against gravity modes. We are eagerly waiting the results of observational searches for luminosity variations in these stars.Comment: 4-page letter + 4 figure

A different kind of quantum search

The quantum search algorithm consists of an alternating sequence of selective inversions and diffusion type operations, as a result of which it can find a target state in an unsorted database of size N in only sqrt(N) queries. This paper shows that by replacing the selective inversions by selective phase shifts of Pi/3, the algorithm gets transformed into something similar to a classical search algorithm. Just like classical search algorithms this algorithm has a fixed point in state-space toward which it preferentially converges. In contrast, the original quantum search algorithm moves uniformly in a two-dimensional state space. This feature leads to robust search algorithms and also to conceptually new schemes for error correction.Comment: 13 pages, 4 figure

Quantum computers can search rapidly by using almost any selective transformations

The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a classical computer. The algorithm uses selective transformations to distinguish the initial state and target state from other states. It does not succeed unless the selective transformations are very close to phase-inversions. Here we show a way to go beyond this limitation. An important application lies in quantum error-correction, where the errors can cause the selective transformations to deviate from phase-inversions. The algorithms presented here are robust to errors as long as the errors are reproducible and reversible. This particular class of systematic errors arise often from imperfections in apparatus setup. Hence our algorithms offer a significant flexibility in the physical implementation of quantum search.Comment: 8 pages, Accepted for publication in PR

Quantum Computation of a Complex System : the Kicked Harper Model

The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near-integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected, and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection, whereas others are exponentially sensitive to imperfection strength. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as 7-8 qubits, and can be reliably measured in presence of moderate levels of internal imperfections

Exponential quantum enhancement for distributed addition with local nonlinearity

We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to take place through a specific apparatus which enforces the constraints that all nonlinear, nonlocal classical logic is performed by a single receiver, and that all communication occurs through a limited number of one-bit channels. In the entanglement-assisted version, the number of channels required to compute a Boolean function of fixed nonlinearity can become exponentially smaller than in the classical version. We demonstrate this exponential enhancement for the problem of distributed integer addition.Comment: To appear in Quantum Information Processin

Quantum Bit String Commitment

A bit string commitment protocol securely commits $N$ classical bits in such a way that the recipient can extract only $M<N$ bits of information about the string. Classical reasoning might suggest that bit string commitment implies bit commitment and hence, given the Mayers-Lo-Chau theorem, that non-relativistic quantum bit string commitment is impossible. Not so: there exist non-relativistic quantum bit string commitment protocols, with security parameters $\epsilon$ and $M$, that allow $A$ to commit $N = N(M, \epsilon)$ bits to $B$ so that $A$'s probability of successfully cheating when revealing any bit and $B$'s probability of extracting more than $N'=N-M$ bits of information about the $N$ bit string before revelation are both less than $\epsilon$. With a slightly weakened but still restrictive definition of security against $A$, $N$ can be taken to be $O(\exp (C N'))$ for a positive constant $C$. I briefly discuss possible applications.Comment: Published version. (Refs updated.

Cheat Sensitive Quantum Bit Commitment

We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We give an example of an unconditionally secure cheat sensitive non-relativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.Comment: Final version: a slightly shortened version of this will appear in PRL. Minor corrections from last versio

Multi-Party Pseudo-Telepathy

Quantum entanglement, perhaps the most non-classical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a variety of distributed computational tasks. We speak of pseudo-telepathy when quantum entanglement serves to eliminate the classical need to communicate. In earlier examples of pseudo-telepathy, classical protocols could succeed with high probability unless the inputs were very large. Here we present a simple multi-party distributed problem for which the inputs and outputs consist of a single bit per player, and we present a perfect quantum protocol for it. We prove that no classical protocol can succeed with a probability that differs from 1/2 by more than a fraction that is exponentially small in the number of players. This could be used to circumvent the detection loophole in experimental tests of nonlocality.Comment: 11 pages. To be appear in WADS 2003 proceeding