Practical sharing of quantum secrets over untrusted channels

In this work we address the issue of sharing a quantum secret over untrusted channels between the dealer and players. Existing methods require entanglement over a number of systems which scales with the security parameter, quickly becoming impractical. We present protocols (interactive and a non-interactive) where single copy encodings are sufficient. Our protocols work for all quantum secret sharing schemes and access structures, and are implementable with current experimental set ups. For a single authorised player, our protocols act as quantum authentication protocols

Authenticated teleportation with one-sided trust

We introduce a protocol for authenticated teleportation, which can be proven secure even when the receiver does not trust their measurement devices, and is experimentally accessible. We use the technique of self-testing from the device-independent approach to quantum information, where we can characterise quantum states and measurements from the exhibited classical correlations alone. First, we derive self-testing bounds for the Bell state and Pauli $\sigma_X, \sigma_Z$ measurements, that are robust enough to be implemented in the lab. Then, we use these to determine a lower bound on the fidelity of an untested entangled state to be used for teleportation. Finally, we apply our results to propose an experimentally feasible protocol for one-sided device-independent authenticated teleportation. This can be interpreted as a first practical authentication of a quantum channel, with additional one-sided device-independence.Comment: published versio

Local encoding of classical information onto quantum states

In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an encoding, this includes all stabilizer states such as cluster states and all graph states. We also show encoding for classes of symmetric states (which cannot be generated by Clifford operations). We generalise our approach using group theoretic methods introducing the unifying notion of Pseudo Clifford operations. All states generated by Pseudo Clifford operations are locally encodable (unifying all our examples), and we give a general method for generating sets of many such locally encodable states.Comment: 10 pages, 4 figures. Version II. Missing references added, minor simplification of theorem and minor errors corrected. Published in a special issue of Journal of Modern Optics celebrating the 60th birthday of Peter Knigh

Efficient approximate unitary t-designs from partially invertible universal sets and their application to quantum speedup

At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct new families of quantum circuits on $n$-qubits giving rise to $\varepsilon$-approximate unitary $t$-designs efficiently in $O(n^3t^{12})$ depth. These quantum circuits are based on a relaxation of technical requirements in previous constructions. In particular, the construction of circuits which give efficient approximate $t$-designs by Brandao, Harrow, and Horodecki (F.G.S.L Brandao, A.W Harrow, and M. Horodecki, Commun. Math. Phys. (2016).) required choosing gates from ensembles which contained inverses for all elements, and that the entries of the unitaries are algebraic. We reduce these requirements, to sets that contain elements without inverses in the set, and non-algebraic entries, which we dub partially invertible universal sets. We then adapt this circuit construction to the framework of measurement based quantum computation(MBQC) and give new explicit examples of $n$-qubit graph states with fixed assignments of measurements (graph gadgets) giving rise to unitary $t$-designs based on partially invertible universal sets, in a natural way. We further show that these graph gadgets demonstrate a quantum speedup, up to standard complexity theoretic conjectures. We provide numerical and analytical evidence that almost any assignment of fixed measurement angles on an $n$-qubit cluster state give efficient $t$-designs and demonstrate a quantum speedup.Comment: 25 pages,7 figures. Comments are welcome. Some typos corrected in newest version. new References added.Proofs unchanged. Results unchange

Adiabatic graph-state quantum computation

Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any measurement-based quantum computation on a graph state with \emph{gflow} can be converted into an adiabatically driven holonomic computation, which we call \emph{adiabatic graph-state quantum computation} (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of $\dot{H}$ as well as the degree of $H$, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated.Comment: 25 pages, 3 figure

Entanglement and symmetry in permutation symmetric states

We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the representation under rotation is equivalent to symmetry of the states under products of local unitaries. The geometric measure of entanglement is thus phrased entirely as a geometric optimisation, and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally we see that different symmetries of the states correspond to different types of entanglement with respect to SLOCC interconvertibility.Comment: 4 pages, 2 figures. Preliminary versions of some of these results were presented in the QIT 16 workshop in Japan, D. Markham, Proceedings of QIT 16, Japan (2007). Updated to reflect changes for publication: expanded proofs and some new examples give

Scheme for constructing graphs associated with stabilizer quantum codes

We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code; second, the canonical form of the CWS code is uncovered; third, the input vertices are attached to the graphs. To check the effectiveness of the scheme, we discuss several graphical constructions of various useful stabilizer codes characterized by single and multi-qubit encoding operators. In particular, the error-correcting capabilities of such quantum codes are verified in graph-theoretic terms as originally advocated by Schlingemann and Werner. Finally, possible generalizations of our scheme for the graphical construction of both (stabilizer and nonadditive) nonbinary and continuous-variable quantum codes are briefly addressed.Comment: 42 pages, 12 figure