New Trends in Quantum Computing

Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantum computing, quantum cryptography and quantum teleportation. Some of the applications range from helping to preventing spies from reading private communications. Among the tools that will facilitate their implementation, we note quantum purification and quantum error correction. Although some of these ideas are still beyond the grasp of current technology, quantum cryptography has been implemented and the prospects are encouraging for small-scale prototypes of quantum computation devices before the end of the millennium.Comment: 8 pages. Presented at the 13th Symposium on Theoretical Aspects of Computer Science, Grenoble, 22 February 1996. Will appear in the proceedings, Lecture Notes in Computer Science, Springer-Verlag. Standard LaTeX. Requires llncs.sty (included

Teleportation as a quantum computation

An explicit quantum circuit is given to implement quantum teleportation. This circuit makes teleportation straightforward to anyone who believes that quantum computation is a reasonable proposition. It could also be genuinely used inside a quantum computer if teleportation is needed to move quantum information around. An unusual feature of this circuit is that there are points in the computation at which the quantum information can be completely disrupted by a measurement (or some types of interaction with the environment) without ill effects: the same final result is obtained whether or not these measurements takes place.Comment: 3 pages, LaTeX2e, PhysComp 96 submissio

Brief History of Quantum Cryptography: A Personal Perspective

Quantum cryptography is the only approach to privacy ever proposed that allows two parties (who do not share a long secret key ahead of time) to communicate with provably perfect secrecy under the nose of an eavesdropper endowed with unlimited computational power and whose technology is limited by nothing but the fundamental laws of nature. This essay provides a personal historical perspective on the field. For the sake of liveliness, the style is purposely that of a spontaneous after-dinner speech.Comment: 14 pages, no figure

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

On local-hidden-variable no-go theorems

The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell inequalities, Bell inequalities without inequalities and pseudo-telepathy. A discussion of the similarities and differences will follow.Comment: 7 pages, no figure, replaced "Bell inequalities" with "Bell theorems" and updated the reference

On The Power of Exact Quantum Polynomial Time

We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines can solve problems that would take exponential time on any classical bounded-error probabilistic computer.Comment: 10 pages, LaTeX2e, no figure

An Exact Quantum Polynomial-Time Algorithm for Simon's Problem

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's problem can be solved in this way, whereas previous algorithms required quantum polynomial time in the expected sense only, without upper bounds on the worst-case running time. This is achieved by generalizing both Simon's and Grover's algorithms and combining them in a novel way. It follows that there is a decision problem that can be solved in exact quantum polynomial time, which would require expected exponential time on any classical bounded-error probabilistic computer if the data is supplied as a black box.Comment: 12 pages, LaTeX2e, no figures. To appear in Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems (ISTCS'97

On the power of non-local boxes

A non-local box is a virtual device that has the following property: given that Alice inputs a bit at her end of the device and that Bob does likewise, it produces two bits, one at Alice's end and one at Bob's end, such that the XOR of the outputs is equal to the AND of the inputs. This box, inspired from the CHSH inequality, was first proposed by Popescu and Rohrlich to examine the question: given that a maximally entangled pair of qubits is non-local, why is it not maximally non-local? We believe that understanding the power of this box will yield insight into the non-locality of quantum mechanics. It was shown recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able to simulate correlations from any measurement on a singlet state. Here, we show that the non-local box can in fact do much more: through the simulation of the magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we show that the non-local box can simulate quantum correlations that no entangled pair of qubits can in a bipartite scenario and even in a multi-party scenario. Finally we show that a single non-local box cannot simulate all quantum correlations and propose a generalization for a multi-party non-local box. In particular, we show quantum correlations whose simulation requires an exponential amount of non-local boxes, in the number of maximally entangled qubit pairs.Comment: 14 pages, 1 figur