Weak randomness completely trounces the security of QKD

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels

Entanglement swapping between multi-qudit systems

We generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number $q$ of systems composed from an arbitrary number $m_j$ of qudits. Each of the system is supposed to be prepared in a maximally entangled state of $m_j$ qudits, while different systems are not correlated at all. We show that when a set $\sum_{j=1}^q a_j$ particles (from each of the $q$ systems $a_j$ particles are measured) are subjected to a generalized Bell-type measurement, the resulting set of $\sum_{j=1}^q (m_j-a_j)$ particles will collapse into a maximally entangled state

Trajectories in the Context of the Quantum Newton's Law

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed, to appear in Physica Script

Purification and correlated measurements of bipartite mixed states

We prove that all purifications of a non-factorable state (i.e., the state which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are entangled. We also show that for any bipartite state there exists a pair of measurements which are correlated on this state if and only if the state is non-factorable.Comment: 4 revtex pages, to appear in Phys. Rev.

The Relativistic Quantum Motions

Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we plot the relativistic quantum trajectories of a particle moving under the constant and the linear potentials. We establish the existence of nodes and link them to the de Broglie's wavelength.Comment: Latex, 18 pages, 3 eps figure

Fair and optimistic quantum contract signing

We present a fair and optimistic quantum contract signing protocol between two clients that requires no communication with the third trusted party during the exchange phase. We discuss its fairness and show that it is possible to design such a protocol for which the probability of a dishonest client to cheat becomes negligible, and scales as N^{-1/2}, where N is the number of messages exchanged between the clients. Our protocol is not based on the exchange of signed messages: its fairness is based on the laws of quantum mechanics. Thus, it is abuse-free, and the clients do not have to generate new keys for each message during the Exchange phase. We discuss a real-life scenario when the measurement errors and qubit state corruption due to noisy channels occur and argue that for real, good enough measurement apparatus and transmission channels, our protocol would still be fair. Our protocol could be implemented by today's technology, as it requires in essence the same type of apparatus as the one needed for BB84 cryptographic protocol. Finally, we briefly discuss two alternative versions of the protocol, one that uses only two states (based on B92 protocol) and the other that uses entangled pairs, and show that it is possible to generalize our protocol to an arbitrary number of clients.Comment: 11 pages, 2 figure

Optimality of private quantum channels

We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel $\cal E$ and von Neumann entropy of the ciphertext state $\varrho^{(0)}$. Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.Comment: no commen

Preparation of polarization entangled mixed states of two photons

We propose a scheme for preparing arbitrary two photons polarization entangled mixed states via controlled location decoherence. The scheme uses only linear optical devices and single-mode optical fibers, and may be feasible in experiment within current optical technology.Comment: 3 pages, 5 figs. The article has been rewritten. Discussion about experiment are added. To appear in Phys. Rev.

A framework for estimating society’s economic welfare following the introduction of an animal disease: the case of Johne’s disease

Animal diseases are global issues affecting the productivity and financial profitability of affected farms. Johne’s disease is distributed on farms worldwide and is an endemic contagious bacterial infection in ruminants caused by Mycobacterium avium subspecies paratuberculosis. In cattle, the clinical disease manifests itself as chronic enteritis resulting in reduced production, weight loss, and eventually death. Johne’s disease is prevalent in the UK, including Scotland. Direct costs and losses associated with Johne’s disease have been estimated in previous research, confirming an important economic impact of the disease in UK herds. Despite this, the distributional impact of Johne’s disease among milk consumers and producers in Scotland has not been estimated. In this paper, we evaluate the change in society’s economic welfare, namely to dairy producers (i.e. infected and uninfected herds) and milk consumers in Scotland induced by the introduction of Johne’s disease in the national Scottish dairy herd. At the national-level, we conclude that the economic burden falls mainly on producers of infected herds and, to a lesser extent, milk consumers, while producers of uninfected herds benefit from the presence of Johne’s. An infected producer’s loss per cow is approximately two times larger in magnitude than that of an uninfected producer’s gain. Such economic welfare estimates are an important comparison of the relative costs of national herd prevalence and the wider economic welfare implications for both producers and consumers. This is particularly important from a policy, public good, cost sharing, and human health perspective. The economic welfare framework presented in this paper can be applied to other diseases to examine the relative burden of society’s economic welfare of alternative livestock disease scenarios. In addition, the sensitivity analysis evaluates uncertainty in economic welfare given limited data and uncertainty in the national herd prevalence, and other input parameters, associated with Johne’s disease in Scotland. Therefore, until the prevalence of Johne’s is better understood, the full economic cost to Scottish dairy herds remains uncertain but in the meantime the sensitivity analysis evaluates the robustness of economic welfare to such uncertainties