- We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local coupling of the system to a large thermal bath. Two temperature regimes are considered. First we clarify how in the low temperature regime, the thermalization time is governed by a generalization of the energy barrier between orthogonal ground states. When no energy barrier is present the Hamiltonian thermalizes in a time that is at most quadratic in the system size. Secondly, we show that above a universal critical temperature, every stabilizer Hamiltonian relaxes to its unique thermal state in a time which scales at most linearly in the size of the system. We provide an explicit lower bound on the critical temperature. Finally, we discuss the implications of these result for the problem of self-correcting quantum memories with stabilizer Hamiltonians.
- May 29 2015 quant-ph arXiv:1505.07802v1We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.
- Digital signatures are widely used in electronic communications to secure important tasks such as financial transactions, software updates, and legal contracts. The signature schemes that are in use today are based on public-key cryptography and derive their security from computational assumptions. However, it is possible to construct unconditionally secure signature protocols. In particular, using quantum communication, it is possible to construct signature schemes with security based on fundamental principles of quantum mechanics. Several quantum signature protocols have been proposed, but none of them has been explicitly generalized to more than three participants, and their security goals have not been formally defined. Here, we first extend the security definitions of Swanson and Stinson (2011) so that they can apply also to the quantum case, and introduce a formal definition of transferability based on different verification levels. We then prove several properties that multiparty signature protocols with information-theoretic security -- quantum or classical -- must satisfy in order to achieve their security goals. We also express two existing quantum signature protocols with three parties in the security framework we have introduced. Finally, we generalize a quantum signature protocol given in Wallden-Dunjko-Kent-Andersson (2015) to the multiparty case, proving its security against forging, repudiation and non-transferability. Notably, this protocol can be implemented using any point-to-point quantum key distribution network and therefore is ready to be experimentally demonstrated.
- In this note we show that the random homological product code construction of Bravyi and Hastings can be extended to qudits of dimension D with D an odd prime. While the result is not surprising, the proof does require new ideas.
- May 29 2015 quant-ph arXiv:1505.07535v1We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and therefore Alice can obtain the correct computation result. Regarding the security, whatever Bob does, Bob cannot learn any information about Alice's computation because of the no-signaling principle. Furthermore, evil Bob does not necessarily send the copies of the correct graph state, but Alice can check the correctness of Bob's state by directly verifying stabilizers of some copies.
- May 29 2015 q-bio.PE arXiv:1505.07821v1Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should, as John Maynard Smith famously pointed out, strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps - RNA SS, HP for tertiary, Polyominoes for protein quaternary structure - to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain (mutationally neutral) genotypes mapping to the same phenotype than in the random null model. These neutral correlations can increase the robustness to mutations by orders of magnitude over that of the null model, raising robustness above the critical threshold for the formation of large neutral networks that enhance the capacity for neutral exploration. We also study \em non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.
- In this paper, a family of three-weight binary linear codes is constructed. Some of the linear codes obtained are either optimal or almost optimal. These codes have applications in association schemes, authentication codes, and secret sharing schemes, in addition to their usages in consumer electronics, communication and data storage systems.
- May 29 2015 quant-ph arXiv:1505.07653v1Parity measurement is a key step in many entanglement generation and quantum error correction schemes. We propose a protocol for non-destructive parity measurement of two remote qubits, i.e., macroscopically separated qubits with no direct interaction. The qubits are instead dispersively coupled to separate resonators that radiate to shared photodetectors. The scheme is deterministic in the sense that there is no fundamental bound on the success probability. Compared to previous proposals, our protocol addresses the scenario where number resolving photodetectors are available but the qubit-resonator coupling is time-independent and only dispersive.
- We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with optimal play on percolation clusters of Euclidean lattices. On Z^2 with two different percolation parameters for odd and even sites, we prove that the game has no draws provided closed sites of one parity are sufficiently rare compared with those of the other parity (thus favoring one player). We prove this also for certain d-dimensional lattices with d>=3. It is an open question whether draws can occur when the two parameters are equal. On a finite ball of Z^2, with only odd sites closed but with the external boundary consisting of even sites, we identify up to logarithmic factors a critical window for the trade-off between the size of the ball and the percolation parameter. Outside this window, one or other player has a decisive advantage. Our analysis of the game is intimately tied to the effect of boundary conditions on maximum-cardinality matchings.
- May 29 2015 math.CA arXiv:1505.07822v1
- May 29 2015 astro-ph.EP arXiv:1505.07820v1
- May 29 2015 math.AG arXiv:1505.07819v1
- May 29 2015 hep-ph arXiv:1505.07817v1
- May 29 2015 math.CA arXiv:1505.07816v1
- May 29 2015 quant-ph physics.atom-ph arXiv:1505.07815v1
- May 29 2015 cs.NE arXiv:1505.07814v1
- May 29 2015 cond-mat.mtrl-sci arXiv:1505.07813v1
- May 29 2015 astro-ph.SR arXiv:1505.07808v1
- May 29 2015 astro-ph.IM astro-ph.SR arXiv:1505.07806v1
- May 29 2015 hep-ph arXiv:1505.07805v1
- May 29 2015 cs.GR arXiv:1505.07804v1
- May 29 2015 hep-th arXiv:1505.07803v1
- May 29 2015 physics.ed-ph arXiv:1505.07801v1
- May 29 2015 stat.ME arXiv:1505.07798v1
- May 29 2015 hep-th arXiv:1505.07797v1
- May 29 2015 cond-mat.supr-con arXiv:1505.07796v1
- May 29 2015 math.NA arXiv:1505.07795v1
- May 29 2015 cs.LO arXiv:1505.07794v1
- May 29 2015 physics.bio-ph q-bio.TO arXiv:1505.07792v1
- May 29 2015 cond-mat.mes-hall arXiv:1505.07791v1
- May 29 2015 math.DG arXiv:1505.07790v1
- May 29 2015 nucl-th astro-ph.SR arXiv:1505.07789v1
- Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measureMay 29 2015 math.CA arXiv:1505.07788v1
- May 29 2015 math.GR arXiv:1505.07786v1
- May 29 2015 math.AG arXiv:1505.07784v1
- May 29 2015 cs.HC arXiv:1505.07783v1
- May 29 2015 math.CT arXiv:1505.07782v1
- May 29 2015 cs.DM arXiv:1505.07780v1