No purification for two copies of a noisy entangled state

We consider whether two copies of a noisy entangled state can be transformed into a single copy of greater purity using local operations and classical communication. We show that it is never possible to achieve such a purification with certainty when the family of noisy states is twirlable (i.e. when there exists a local transformation that maps all states into the family, yet leaves the family itself invariant). This implies that two copies of a Werner state cannot be deterministically purified. Furthermore, due to the construction of the proof, it will hold not only in quantum theory, but in any generalised probabilistic theory. We use this to show that two copies of a noisy PR-box (a hypothetical device more non-local than is allowed by quantum theory) cannot be purified.Comment: 4 pages, 2 figure

Classical simulation of limited-width cluster-state quantum computation

We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We use this result to show that any log-depth quantum computation in the gate array model, with gates linking only nearby qubits, can be simulated efficiently on a classical computer.Comment: 4 pages, 1 figur

Efficient classical simulation of the approximate quantum Fourier transform

We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in polynomial time. Moreover, our approach allows us to formulate a condition for the composability of simulable quantum circuits. We use this condition to show that any circuit composed of a constant number of approximate quantum Fourier transform circuits and log-depth circuits with limited interaction range can also be efficiently simulated.Comment: 5 pages, 3 figure

Causal Fermions in Discrete Spacetime

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.Comment: 16 pages, 1 figur

Discrete Spacetime and Relativistic Quantum Particles

We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform a simple relabeling of the coordinate axes or demand rotational symmetry in the continuum limit. It is surprising that this occurs regardless of the specific details of the evolution: it would be natural to assume that discrete evolutions giving rise to relativistic dynamics in the continuum limit would be very special cases. We also see that the same is not true for particles with larger internal degrees of freedom, by looking at an example with a three dimensional internal degree of freedom that is not relativistic in the continuum limit. In the process we give a formula for the Hamiltonian arising from the continuum limit of massless and massive particles in discrete spacetime.Comment: 6 page

An exploration of the methods used by external coaches when coaching IT professionals

This study explored the research question: Do external coaches use an alternative method to their norm when coaching IT professionals? The aim of this research was to explore whether executive coaches work differently with clients who are IT professionals than with clients from other disciplines. The word ‘method’ in the research question describes how coaches work with clients and includes the model, style and tools. The literature was reviewed across the component parts of this aim. The data from experienced executive coaches working externally to organisations, when coaching IT professionals, combined with this literature helped answer the research question. Within coach development approach, models and ethics are usually addressed; however, there is little consideration given to the impact of differences within disciplines across organisations. No academic papers on coaching in the IT sector were found but there was some reference within practitioner literature which has been included. Semi-structured interviews with seven experienced external coaches, were carried out to collect the rich data needed. Thematic analysis allowed references to be gathered around four superordinate themes; Coaching Style, IT Professionals Pattern of Behaviour, Process and Relationship. This research has shown clear differences in the method of coaching of IT professionals. Within the process of coaching, the relationship tends to develop after a critical moment in the coaching that then allows engagement of the client. The data reveals that this population are reluctant clients initially (Moore, Kambitsis and Seward, 2013). This reluctance is present both when “sent” by their organisation or self-referring. The preferred coach style identified by coaches for these clients is highly directive and challenging rather than emotional and non-direct. This research has identified an alternative framework for coaching for these clients