Random quantum channels I: graphical calculus and the Bell state phenomenon

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an application, we study variations of random matrix models introduced by Hayden \cite{hayden}, and show that their eigenvalues converge almost surely. In particular we obtain for some models sharp improvements on the value of the largest eigenvalue, and this is shown in a further work to have new applications to minimal output entropy inequalities.Comment: Several typos were correcte

Shoreline configuration and shoreline dynamics: A mesoscale analysis

The author has identified the following significant results. Atlantic coast barrier island shorelines are seldom straight, but rather sinuous. These shoreline curvatures range in size from cusps to capes. Significant relationships exist between the orientation of shoreline segments within the larger of these sinuous features and shoreline dynamics, with coefficients ranging up to .9. Orientation of the shoreline segments of Assateague Island (60 km) and the Outer Banks of North Carolina (130 km) was measured from LANDSAT 2 imagery (1:80,000) and high altitude aerial photography (1:120,000). Long term trends in shoreline dynamics were established by mapping shoreline and storm-surge penetration changes

LANDSAT application of remote sensing to shoreline-form analysis

The author has identified the following significant results. Orientation of the shoreline segments of Assateague Island (55 km) was measured from LANDSAT 2 imagery enlarged to 1:250,000 and 1:80,000. Long term trends in shoreline dynamics were established by mapping shoreline and storm-surge penetration changes from historical low altitude aerial photography spanning four decades

Entropy and Entanglement in Quantum Ground States

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.Comment: 7 pages, no figure

Typical entanglement of stabilizer states

How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code. Finally, we show that typically very few GHZ states can be extracted from a random multipartite stabilizer state via local unitary operations. Our main tool is a new concentration inequality which bounds deviations from the mean of random variables which are naturally defined on the Clifford group.Comment: Final version, to appear in PRA. 11 pages, 1 figur

Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field

Using a tilted field geometry, the effect of an in-plane magnetic field on the even denominator nu = 5/2 fractional quantum Hall state is studied. The energy gap of the nu = 5/2 state is found to collapse linearly with the in-plane magnetic field above ~0.5 T. In contrast, a strong enhancement of the gap is observed for the nu = 7/3 state. The radically distinct tilted-field behaviour between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read pfaffian wavefunction for the 5/2 fractional quantum Hall effect

Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State

The fractional quantum Hall effect is observed at low field, in a regime where the cyclotron energy is smaller than the Coulomb interaction. The nu=5/2 excitation gap is measured to be 262+/-15 mK at ~2.6 T, in good agreement with previous measurements performed on samples with similar mobility, but with electronic density larger by a factor of two. The role of disorder on the nu=5/2 gap is examined. Comparison between experiment and theory indicates that a large discrepancy remains for the intrinsic gap extrapolated from the infinite mobility (zero disorder) limit. In contrast, no such large discrepancy is found for the nu=1/3 Laughlin state. The observation of the nu=5/2 state in the low-field regime implies that inclusion of non-perturbative Landau level mixing may be necessary to better understand the energetics of half-filled fractional quantum hall liquids.Comment: 5 pages, 4 figures; typo corrected, comment expande

LANDSAT application of remote sensing to shoreline-form analysis

The author has identified the following significant results. Data for Assateague Island and Ocracoke Island show significantly high correlations between coastal orientation and erosion. However, South Hatteras has low correlations, and North Hatteras has low negative correlations. Because all four areas are essentially in the same mid-Atlantic climatic regime, process/response relationships should be similar. Correlations for the four areas may differ considerably because of inadequate assumptions; the key is the mean orientation of the specific coastline being studied. There appears to be an orientation window surrounding due northeast (135 deg north of south) in which this hypothesis holds