The structure of degradable quantum channels

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions ($d_B$ and $d_E$ respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is "small" in the sense $d_E \leq d_B$. Perhaps surprisingly, we also present examples of degradable channels with ``large'' environments, in the sense that the minimal dimension $d_E > d_B$. Indeed, one can have $d_E > \tfrac{1}{4} d_B^2$. In the case of channels with diagonal Kraus operators, we describe the subclass which are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.Comment: 42 pages, 3 figures, Web and paper abstract differ; (v2 contains only minor typo corrections

Quasi-specular albedo of cold neutrons from powder of nanoparticles

We predicted and observed for the first time the quasi-specular albedo of cold neutrons at small incidence angles from a powder of nanoparticles. This albedo (reflection) is due to multiple neutron small-angle scattering. The reflection angle as well as the half-width of angular distribution of reflected neutrons is approximately equal to the incidence angle. The measured reflection probability was equal to ~30% within the detector angular size that corresponds to 40-50% total calculated probability of quasi-specular reflection

Dilemma In Development, Education And Employment: An Analysis Of Zimbabwe, Tanzania And Kenya

A Zambezia journal article.1979 was a year of impending change — change that was without form or concept. Speculation was rife while planners anxiously awaited policy direction. At that time we felt the need to point out certain realities in Zimbabwe’s education and employment potentiality, and to distinguish facts from the fantasies. In this paper we have identified four major premises which underlie existing educational and employment strategies. We call these ‘conventional wisdoms’; and in them we have tried to pin down the implicit assumptions which too often are taken as ‘givens’. These conventional wisdoms can be summarized as follows: 1. Resources to satisfy the demand for education will be available when the war stops and aid flows in. 2. Education will generate the required wealth and development. 3. People are unemployed because they do not have enough education or training. 4. In the fields of education and employment all that we need to solve our development problems is more of the same

Undecidability of the Spectral Gap in One Dimension

The spectral gap problem—determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations—pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum-spin systems in two (or more) spatial dimensions: There exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one-dimensional spin systems are simpler than their higher-dimensional counterparts: For example, they cannot have thermal phase transitions or topological order, and there exist highly effective numerical algorithms such as the density matrix renormalization group—and even provably polynomial-time ones—for gapped 1D systems, exploiting the fact that such systems obey an entropy area law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper, we prove this is not the case by constructing a family of 1D spin chains with translationally invariant nearest-neighbor interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but it also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with a constant spectral gap and nondegenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behavior with dense spectrum

Extracting dynamical equations from experimental data is NP-hard

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP-hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70 years).Comment: For mathematical details, see arXiv:0908.2128[math-ph]. v2: final version, accepted in Phys. Rev. Let

Improving zero-error classical communication with entanglement

Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behaviour constitutes the field of classical zero-error information theory, the quantum generalisation of which has started to develop recently. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent with no chance of error. In particular, we show how to construct such a channel based on any proof of the Bell-Kochen-Specker theorem. This is a new example of the use of quantum effects to improve the performance of a classical task. We investigate the connection between this phenomenon and that of ``pseudo-telepathy'' games. The use of generalised non-signalling correlations to assist in this task is also considered. In this case, a particularly elegant theory results and, remarkably, it is sometimes possible to transmit information with zero-error using a channel with no unassisted zero-error capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus figure 1 and the non-signalling box exampl

Square vortex lattice at anomalously low magnetic fields in electron-doped Nd1.85_{1.85}Ce0.15_{0.15}CuO4_{4}

We report here on the first direct observations of the vortex lattice in the bulk of electron-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$ single crystals. Using small angle neutron scattering, we have observed a square vortex lattice with the nearest-neighbors oriented at 45$^{\circ}$ from the Cu-O bond direction, which is consistent with theories based on the d-wave superconducting gap. However, the square symmetry persists down to unusually low magnetic fields. Moreover, the diffracted intensity from the vortex lattice is found to decrease rapidly with increasing magnetic field.Comment: 4 pages, 4 Figures, accepted for publication in Phys. Rev. Let

Anisotropic properties of MgB2 by torque magnetometry

Anisotropic properties of superconducting MgB2 obtained by torque magnetometry are compared to theoretical predictions, concentrating on two issues. Firstly, the angular dependence of Hc2 is shown to deviate close to Tc from the dependence assumed by anisotropic Ginzburg-Landau theory. Secondly, from the evaluation of torque vs angle curves it is concluded that the anisotropy of the penetration depth gamma_lambda has to be substantially higher at low temperature than theoretical estimates, at least in fields higher than 0.2 T.Comment: 2 p.,2 Fig., submitted to Physica C (M2S-Rio proceedings); v2: 1 ref adde