DCM on Saturday, July 10th

09:00‑10:00 Session 5
Chair: Elham Kashefi
Location: IF G.07A
09:00 Vlatko Vedral (Oxford University)
Phase Estimation with Mixed States: Quantum Coherence versus Correlations
10:30‑11:30 Session 6
Location: IF G.07A
10:30 Bas Spitters Spitters
The space of measurement outcomes as a non-commutative spectrum

Bohrification defines a locale of hidden variables internal in a topos. We find that externally this is the space of partial measurement outcomes. By considering the not not-sheafification, we obtain the space of measurement outcomes, a genuine generalization of the spectrum of a C*-algebra.

11:00 Mio Murao and Akihito Soeda
Delocalization power of global unitary operations on quantum information

We investigate how originally localized two-pieces of quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization power of global unitary operations on quantum information, we analyze the necessary and sufficient condition to deterministically relocalize one of the two-pieces of quantum information to its original Hilbert space by using only LOCC. We prove that this LOCC one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent to a controlled-unitary operation. The delocalization power and entangling power characterize different non-local properties of global unitary operations.

11:30‑12:30 Session 7
Chair: Barry Cooper
Location: IF G.07A
11:30 Cristian Calude (University of Auckland, New Zealand)
Understanding the Quantum Computational Speed-up via De-quantisation
14:00‑15:00 Session 8
Chair: Elham Kashefi
Location: IF G.07A
14:00 Lucien Hardy (Perimeter Institute for Theoretical Physics)
Operational Computing with Quantum Stuff
15:30‑18:00 Session 9
Location: IF G.07A
15:30 Dominik Floess, Erika Andersson and Mark Hillery
Quantum algorithms for testing Boolean functions

We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.

16:00 Vedran Dunjko and Elham Kashefi
Algebraic characterization of one-way patterns

We give a complete structural characterization of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed to obtain the primary structure of the matrix M, representing the phase map decomposition in the computational basis. Using this approach we obtain some preliminary results on the connection between the columns structure of a given unitary and the angles of measurements in a pattern that implements it. We believe this work is a step forward towards a full characterisation of those unitaries with an efficient one-way model implementation.

16:30 Lucas Dixon, Ross Duncan and Aleks Kissinger
Open Graphs and Computational Reasoning

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

17:00 Abolfazl Bayat, Pasquale Sodano and Sougato Bose
Entanglement in the Kondo Spin Chain

We consider an impurity at one end of a spin chain. This model is known to realize a Kondo system and we find that a genuine entanglement measure can be used to capture the extent of the Kondo cloud. The essential scaling of the entanglement is found to be independent of the system size depending only on ratios of the sizes to the Kondo length.

From a practical perspective, entanglement between the impurity and a block of spins is a useless entanglement. To convert this useless entanglement into a useful one we quench a single bond at one end of the spin chain and we show that this quickly establishes a high quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by a Kondo cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. This quench approach paves the way to detect the elusive Kondo cloud through the entanglement between two individual spins.

17:30 Janet Anders, Stefanie Hilt, Saroosh Shabbir and Eric Lutz
Landauer’s principle in the quantum domain

Recent papers discussing thermodynamic processes in strongly coupled quantum systems claim a violation of Landauer’s principle and imply a violation of the second law of thermodynamics [1, 2, 3, 4]. If true, this would have powerful consequences. Perpetuum mobiles could be build as long as the operating temperature is brought close to zero. It would also have serious consequences on thermodynamic derivations of information theoretic results, such as the Holevo bound [5]. Here we argue why these claims are erroneous. Correlations occurring in the strongly coupled, quantum domain require a rethink of how entropy, heat and work are calculated. It is shown that a consistent treatment solves the paradox [6].