Security of Quantum Bit-String Generation

We consider the cryptographic task of bit-string generation. This is a generalisation of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analysed in this paper has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A corresponding experiment is reported in quant-ph/040812

Modeling Pauli measurements on graph states with nearest-neighbor classical communication

We propose a communication-assisted local-hidden-variable model that yields the correct outcome for the measurement of any product of Pauli operators on an arbitrary graph state, i.e., that yields the correct global correlation among the individual measurements in the Pauli product. Within this model, communication is restricted to a single round of message passing between adjacent nodes of the graph. We show that any model sharing some general properties with our own is incapable, for at least some graph states, of reproducing the expected correlations among all subsets of the individual measurements. The ability to reproduce all such correlations is found to depend on both the communication distance and the symmetries of the communication protocol.Comment: 9 pages, 2 figures. Version 2 significantly revised. Now includes a site-invariant protocol for linear chains and a proof that no limited communication protocol can correctly predict all quantum correlations for ring

Quantum coin tossing and bit-string generation in the presence of noise

We discuss the security implications of noise for quantum coin tossing protocols. We find that if quantum error correction can be used, so that noise levels can be made arbitrarily small, then reasonable security conditions for coin tossing can be framed so that results from the noiseless case will continue to hold. If, however, error correction is not available (as is the case with present day technology), and significant noise is present, then tossing a single coin becomes problematic. In this case, we are led to consider random n-bit string generation in the presence of noise, rather than single-shot coin tossing. We introduce precise security criteria for n-bit string generation and describe an explicit protocol that could be implemented with present day technology. In general, a cheater can exploit noise in order to bias coins to their advantage. We derive explicit upper bounds on the average bias achievable by a cheater for given noise levels.Comment: REVTeX. 6 pages, no figures. Early versions contained errors in statements of security conditions, although results were correct. v4: PRA versio

No Signalling and Quantum Key Distribution

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use post-quantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a post-quantum eavesdropper who is limited only by the impossibility of superluminal signalling. The security of the scheme stems from violation of a Bell inequality.Comment: Clarifications and minor revisions in response to comments. Final version; to appear in Phys. Rev. Let

Oakleaf: an S locus-linked mutation of Primula vulgaris that affects leaf and flower development

•In Primula vulgaris outcrossing is promoted through reciprocal herkogamy with insect-mediated cross-pollination between pin and thrum form flowers. Development of heteromorphic flowers is coordinated by genes at the S locus. To underpin construction of a genetic map facilitating isolation of these S locus genes, we have characterised Oakleaf, a novel S locus-linked mutant phenotype. •We combine phenotypic observation of flower and leaf development, with classical genetic analysis and next-generation sequencing to address the molecular basis of Oakleaf. •Oakleaf is a dominant mutation that affects both leaf and flower development; plants produce distinctive lobed leaves, with occasional ectopic meristems on the veins. This phenotype is reminiscent of overexpression of Class I KNOX-homeodomain transcription factors. We describe the structure and expression of all eight P. vulgaris PvKNOX genes in both wild-type and Oakleaf plants, and present comparative transcriptome analysis of leaves and flowers from Oakleaf and wild-type plants. •Oakleaf provides a new phenotypic marker for genetic analysis of the Primula S locus. We show that none of the Class I PvKNOX genes are strongly upregulated in Oakleaf leaves and flowers, and identify cohorts of 507 upregulated and 314 downregulated genes in the Oakleaf mutant

Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality

We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) on a class of entangled generalized Werner states, thus demonstrating that such measurements do not always violate a Bell-type inequality. We also show that, in general, if the state $\rho'$ can be obtained from $\rho$ with certainty by local quantum operations without classical communication then an LHVPOV model for the state $\rho$ implies the existence of such a model for $\rho'$.Comment: 4 pages, no figures. Title changed to accord with Phys. Rev. A version. Journal reference adde

Genomic comparison of diverse Salmonella serovars isolated from swine.

Food animals act as a reservoir for many foodborne pathogens. Salmonella enterica is one of the leading pathogens that cause food borne illness in a broad host range including animals and humans. They can also be associated with a single host species or a subset of hosts, due to genetic factors associated with colonization and infection. Adult swine are often asymptomatic carriers of a broad range of Salmonella servoars and can act as an important reservoir of infections for humans. In order to understand the genetic variations among different Salmonella serovars, Whole Genome Sequences (WGS) of fourteen Salmonella serovars from swine products were analyzed. More than 75% of the genes were part of the core genome in each isolate and the higher fraction of gene assign to different functional categories in dispensable genes indicated that these genes acquired for better adaptability and diversity. High concordance (97%) was detected between phenotypically confirmed antibiotic resistances and identified antibiotic resistance genes from WGS. The resistance determinants were mainly located on mobile genetic elements (MGE) on plasmids or integrated into the chromosome. Most of known and putative virulence genes were part of the core genome, but a small fraction were detected on MGE. Predicted integrated phage were highly diverse and many harbored virulence, metal resistance, or antibiotic resistance genes. CRISPR (Clustered regularly interspaced short palindromic repeats) patterns revealed the common ancestry or infection history among Salmonella serovars. Overall genomic analysis revealed a great deal of diversity among Salmonella serovars due to acquired genes that enable them to thrive and survive during infection

Countering Quantum Noise with Supplementary Classical Information

We consider situations in which i) Alice wishes to send quantum information to Bob via a noisy quantum channel, ii) Alice has a classical description of the states she wishes to send and iii) Alice can make use of a finite amount of noiseless classical information. After setting up the problem in general, we focus attention on one specific scenario in which Alice sends a known qubit down a depolarizing channel along with a noiseless cbit. We describe a protocol which we conjecture is optimal and calculate the average fidelity obtained. A surprising amount of structure is revealed even for this simple case which suggests that relationships between quantum and classical information could in general be very intricate.Comment: RevTeX, 5 pages, 2 figures Typo in reference 9 correcte

Quantum Common Causes and Quantum Causal Models

Reichenbach’s principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach’s principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach’s principle to a formalism for quantum causal models and provide examples of how the formalism works

Implications of Teleportation for Nonlocality

Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (2000)], we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using `Werner states' of the form x P + (1-x) I/4, where P is the projector corresponding to a singlet state and I is the identity. We find that our inequality is violated, implying nonlocality, if x > 1/sqrt(2). In addition, we extend Werner's local hidden variable model to simulation of teleportation with the x = 1/2 Werner state. Thus teleportation using this state does not involve nonlocality even though the fidelity achieved is 3/4 which is greater than the `classical limit' of 2/3. Finally, we comment on a result of Gisin's and offer some philosophical remarks on teleportation and nonlocality generally.Comment: 10 pages, no figures. Title changed to accord with Phys. Rev. A version. A note and an extra reference have been added. Journal reference adde