Atemporal diagrams for quantum circuits

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using PSTrick

Fair Loss-Tolerant Quantum Coin Flipping

Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a novel quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.Comment: 12 pages, 1 figure; various minor typos corrected in version

Low Cost and Compact Quantum Cryptography

We present the design of a novel free-space quantum cryptography system, complete with purpose-built software, that can operate in daylight conditions. The transmitter and receiver modules are built using inexpensive off-the-shelf components. Both modules are compact allowing the generation of renewed shared secrets on demand over a short range of a few metres. An analysis of the software is shown as well as results of error rates and therefore shared secret yields at varying background light levels. As the system is designed to eventually work in short-range consumer applications, we also present a use scenario where the consumer can regularly 'top up' a store of secrets for use in a variety of one-time-pad and authentication protocols.Comment: 18 pages, 9 figures, to be published in New Journal of Physic

A Lower Bound for Quantum Phase Estimation

We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example in Shor's order finding algorithm. In this setting we will prove a log (1/epsilon) lower bound for the number of applications of Q^p1, Q^p2, ... This bound is tight due to a matching upper bound. We obtain the lower bound using a new technique based on frequency analysis.Comment: 7 pages, 1 figur

Optimal eavesdropping on QKD without quantum memory

We consider the security of the BB84, six-state and SARG04 quantum key distribution protocols when the eavesdropper doesn't have access to a quantum memory. In this case, Eve's most general strategy is to measure her ancilla with an appropriate POVM designed to take advantage of the post-measurement information that will be released during the sifting phase of the protocol. After an optimization on all the parameters accessible to Eve, our method provides us with new bounds for the security of six-state and SARG04 against a memoryless adversary. In particular, for the six-state protocol we show that the maximum QBER for which a secure key can be extracted is increased from 12.6% (for collective attacks) to 20.4% with the memoryless assumption.Comment: 7 pages, 3 figures. Analysis of six-state and SARG04 QKD protocols adde

Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem

Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem.Comment: 21 page

A two-qubit Bell inequality for which POVM measurements are relevant

A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to projective ones. In particular, the presented Bell inequality requires POVMs in order to be maximally violated by a maximally entangled two-qubit state. This answers a question raised by N. Gisin.Comment: 7 pages, 1 figur

A Quantitative Analysis of the Available Multicolor Photometry for Rapidly Pulsating Hot B Subdwarfs

We present a quantitative and homogeneous analysis of the broadband multicolor photometric data sets gathered so far on rapidly pulsating hot B subdwarf stars. This concerns seven distinct data sets related to six different stars. Our analysis is carried out within the theoretical framework developed by Randall et al., which includes full nonadiabatic effects. The goal of this analysis is partial mode identification, i.e., the determination of the degree index l of each of the observed pulsation modes. We assume possible values of l from 0 to 5 in our calculations. For each target star, we compute a specific model atmosphere and a specific pulsation model using estimates of the atmospheric parameters coming from time-averaged optical spectroscopy. For every assumed value of l, we use a formal chi-squared approach to model the observed amplitude-wavelength distribution of each mode, and we compute a quality-of-fit Q probability to quantify the derived fit and to discriminate objectively between the various solutions. We find that no completely convincing and unambiguous l identification is possible on the basis of the available data, although partial mode discrimination has been reached for 25 out of the 41 modes studied. A brief statistical study of these results suggests that a majority of the modes must have l values of 0, 1, and 2, but also that modes with l = 4 could very well be present while modes with l = 3 appear to be rarer. This is in line with recent results showing that l = 4 modes in rapidly pulsating B subdwarfs have a higher visibility in the optical domain than modes with l = 3. Although somewhat disappointing in terms of mode discrimination, our results still suggest that the full potential of multicolor photometry for l identification in pulsating subdwarfs is within reach.Comment: 59 pages, 18 figures, accepted for publication in the Astrophysical Journal Supplement Serie

Softening of the insulating phase near Tc for the photo-induced insulator-to-metal phase transition in vanadium dioxide

We use optical-pump terahertz-probe spectroscopy to investigate the near-threshold behavior of the photoinduced insulator-to-metal (IM) transition in vanadium dioxide thin films. Upon approaching Tc a reduction in the fluence required to drive the IM transition is observed, consistent with a softening of the insulating state due to an increasing metallic volume fraction (below the percolation limit). This phase coexistence facilitates the growth of a homogeneous metallic conducting phase following superheating via photoexcitation. A simple dynamic model using Bruggeman effective medium theory describes the observed initial condition sensitivity.Comment: accepted for publication in Physical Review Letter

Evidence for a merger of binary white dwarfs: the case of GD 362

GD 362 is a massive white dwarf with a spectrum suggesting a H-rich atmosphere which also shows very high abundances of Ca, Mg, Fe and other metals. However, for pure H-atmospheres the diffusion timescales are so short that very extreme assumptions have to be made to account for the observed abundances of metals. The most favored hypothesis is that the metals are accreted from either a dusty disk or from an asteroid belt. Here we propose that the envelope of GD 362 is dominated by He, which at these effective temperatures is almost completely invisible in the spectrum. This assumption strongly alleviates the problem, since the diffusion timescales are much larger for He-dominated atmospheres. We also propose that the He-dominated atmosphere of GD 362 is likely to be the result of the merger of a binary white dwarf.Comment: 4 pages, 3 figures. Accepted for publication in Astrophysical Journal Letter