QUOXIC

The next meeting will be on Wednesday 9th December at Oxford University Computing Lab, Parks Road, Oxford.

Local information about the Computing Lab can be found here.

QUOXIC is free but please register if you are going to come: email Ross Duncan. If you don't there may not be enough coffee and biscuits, and no one wants that.

QUOXIC attendees may be interested in the QNET Workshop on the foundations of quantum computation, happening on the 10th and 11th of December in exactly the same location! Registration is open until the 7th of December.

Schedule

• 14:00 : Joe Fitzsimons (Oxford)
  "Interactive Proofs for Fun and Profit"
• 15:00 : Oscar Dahlsten (ETH Zurich)
  "The single-shot work value of information"
• 15:30 : Bill Edwards (Oxford)
  "The Group Theoretic Origin of Non-Locality For Qubits"
• 16:00 : COFFEE BREAK
• 16:30 : Dimitris Tsomokos (Royal Holloway)
  "Topological order following a sudden quench"
• 17:00 : Jennifer Hide (Leeds)
  "Detecting Entanglement with Jarzynski's equality"
• 17:30 : Hannu Wichterich (UCL)
  "Block-block entanglement at quantum critical points of spin systems"

Abstracts

In this talk I will provide a brief introduction to the notion of interactive proofs, and discuss how this relates to verification of quantum computers. In particular, I will focus on the problem of whether or not the results of a quantum computer can be classically verified. For problems contained within NP the answer is clearly that they can be verified. There do exist problems, however, inside BQP which are not believed to be contained within NP, and it is unclear how such results can be verified. I will introduce the notion of 'blind quantum computation', and how it can be exploited in the context of verification and interactive proof systems. Blind quantum computation refers to the problem of allowing Alice to have Bob carry out a quantum computation for her such that Bob learns nothing about the computation that he performs. I will introduce a protocol for performing secure blind computation and show that it allows any quantum computation to be verified by a classical prover given to non-communicating quantum provers, or by a semi-classical prover using only a single quantum prover.

It is known from the work of Szilard, Bennett and others that information is necessary to extract work. We consider the work value of information in a single instance of work extraction, and find that there is a risk-reward trade-off in harnessing unpredictable forces. We make a connection between statistical mechanics and the smooth entropy approach. This allows us to derive strikingly simple quantitative statements which hold for internally correlated, finite-sized systems and single-shot work extractions. In general these deviate from the standard expression involving the von Neumann entropy, which only emerges in the appropriate limit.

Dahlsten, Renner, Rieper and Vedral
arxiv.org/0908.0424v1

We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms. We then use this framework to compare two theories: quantum mechanics restricted to qubit stabiliser states and operations, and a toy theory proposed by Spekkens. We discover that viewed within our framework these theories are very similar, but differ in one key aspect - a four element group we term the phase group which emerges naturally within our framework. In the case of the stabiliser theory this group is Z4 while for Spekkens's theory the group is Z2 x Z2. We further show that the structure of this group is intimately involved in a key physical difference between the theories: whether or not they can be modelled by a local hidden variable theory. This is done by establishing a connection between the phase group, and an abstract notion of GHZ state correlations. We go on to formulate precisely how the stabiliser theory and toy theory are 'similar' by defining a notion of 'mutually unbiased qubit theory', noting that all such theories have four element phase groups. Since Z4 and Z2 �Z2 are the only such groups we conclude that the GHZ correlations in this type of theory can only take two forms, exactly those appearing in the stabiliser theory and those appearing in Spekkens's theory. The results point at a classification of local/non-local behaviours by finite Abelian groups, extending beyond qubits to any finitary theory whose observables are all mutually unbiased.

Joint work with Bob Coecke and Rob Spekkens.

In this talk I discuss the dynamical response of a topologically-ordered quantum state to a sudden change of evolution. In particular, I consider that a quantum spin lattice is initialized in the ground state of the Toric Code Model and, subsequently, it is let to evolve under a different Hamiltonian H. Firstly, we determine conditions on the form of H under which the entanglement entropy and the topological entropy of the initial state remain unaffected by the sudden quench. Furthermore, we provide numerical evidence for the influence of other quench Hamiltonians on the topological order using the topological entropy and a new measure, which is based on the similarity between partial states from different topological sectors.

We present a method for detecting the entanglement of a state using non-equilibrium processes. A comparison of relative entropies allows us to construct an entanglement witness. The relative entropy can further be related to the quantum Jarzynski equality, allowing non-equilibrium work to be used in entanglement detection. To exemplify our results, we consider two different spin chains.

In this talk we report on our recent findings on entanglement between large groups of spins at zero temperature (quantum) phase transitions. An analytic study on negativity between non-complementary groups in an infite range interaction model shows that it is explicitly finite and universal in the thermodynamic limit. Results from DMRG in one dimensional (1D) spin chains suggest that this property holds more generally in many body systems at criticality. In 1D the negativity between separated blocks decays with distance in a manner that resembles the decay of correlators of primary fields in the corresponding conformal field theory at finite temperature. We shall attempt an explanation that relies on arguments from quantum thermodynamics.