Unique decompositions, faces, and automorphisms of separable states

Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is dense and open in S_k, and such that each state in V_k has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decompositions for a set of separable states that properly contains V_k. In both cases we describe the associated faces of the space of separable states, which in the first case are simplexes, and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras. As an application of these results, we characterize all affine automorphisms of the convex set of separable states, and all automorphisms of the state space of B(C^m otimes C^n). that preserve entanglement and separability.Comment: Since original version:Cor. 6 revised and renamed Thm 6, some definitions added before Cor. 11, introduction revised and references added, typos correcte

Unconventional antiferromagnetic correlations of the doped Haldane gap system Y2_2BaNi1−x_{1-x}Znx_xO5_5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y$_2$BaNi$_{1-x}$Zn$_x$O$_5$. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility $\chi(T) \sim C / (\Theta+T)$ as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the ``impurity'' susceptibility $\chi_{imp}(T)$ by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by $T \chi_{imp}(T) = C_{imp} (1 + T_{imp}/T )^{-\gamma}$. In the temperature range [100 mK, 1 K] the experimental data are well fitted by $T \chi_{imp}(T) = A \ln{(T/T_c)}$, where $T_c$ increases with $x$. This fit suggests the existence of a finite N\'eel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility $\chi'(T)$ which suggests the existence of antiferromagnetic correlations at very low temperature.Comment: 19 pages, 17 figures, revised version (minor modifications

An automated and versatile ultra-low temperature SQUID magnetometer

We present the design and construction of a SQUID-based magnetometer for operation down to temperatures T = 10 mK, while retaining the compatibility with the sample holders typically used in commercial SQUID magnetometers. The system is based on a dc-SQUID coupled to a second-order gradiometer. The sample is placed inside the plastic mixing chamber of a dilution refrigerator and is thermalized directly by the 3He flow. The movement though the pickup coils is obtained by lifting the whole dilution refrigerator insert. A home-developed software provides full automation and an easy user interface.Comment: RevTex, 10 pages, 10 eps figures. High-resolution figures available upon reques

The effects of nuclear spins on the quantum relaxation of the magnetization for the molecular nanomagnet Fe_8

The strong influence of nuclear spins on resonant quantum tunneling in the molecular cluster Fe_8 is demonstrated for the first time by comparing the relaxation rate of the standard Fe_8 sample with two isotopic modified samples: (i) 56_Fe is replaced by 57_Fe, and (ii) a fraction of 1_H is replaced by 2_H. By using a recently developed "hole digging" method, we measured an intrinsic broadening which is driven by the hyperfine fields. Our measurements are in good agreement with numerical hyperfine calculations. For T > 1.5 K, the influence of nuclear spins on the relaxation rate is less important, suggesting that spin-phonon coupling dominates the relaxation rate at higher temperature.Comment: 4 pages, 5 figure

Classical and nonclassical randomness in quantum measurements

The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives of classical and non-classical convexity through a transform $\Gamma$ that associates any positive operator-valued measure with a certain completely positive linear map of the homogeneous C*-algebra $C(X)\otimes B(H)$ into $B(H)$. This association is achieved by using an operator-valued integral in which non-classical random variables (that is, operator-valued functions) are integrated with respect to positive operator-valued measures and which has the feature that the integral of a random quantum effect is itself a quantum effect. A left inverse $\Omega$ for $\Gamma$ yields an integral representation, along the lines of the classical Riesz Representation Theorem for certain linear functionals on $C(X)$, of certain (but not all) unital completely positive linear maps $\phi:C(X)\otimes B(H) \rightarrow B(H)$. The extremal and C*-extremal points of the space of POVMS are determined.Comment: to appear in Journal of Mathematical Physic

Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_\sigma where \sigma is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_\sigma is a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly specified. Presentation more detailed. Implementing the shift after the dephasing is sometimes more convenien

Distinct mechanisms of Up state maintenance in the medial entorhinal cortex and neocortex

The medial entorhinal cortex (mEC) is a key structure which controls the communication between the hippocampus and the neocortex. During slow-wave sleep, it stands out from other cortical regions by exhibiting persistent activity that outlasts neocortical Up states, decoupling the entorhinal cortex-hippocampal interaction from the neocortex. Here, we compared the mechanisms involved in the maintenance of the Up state in the barrel cortex (BC) and mEC using whole cell recordings in acute mouse brain slices. Bath application of an NMDA receptor antagonist abolished Up states in the BC, and reduced the incidence but not the duration of Up states in the mEC. Conversely, blockade of kainate receptors decreased Up state duration in the mEC, but not in the BC. Voltage clamp recordings demonstrated the presence of a non-NMDA glutamate receptor-mediated slow excitatory postsynaptic current, sensitive to the selective kainate receptor antagonist UBP-302, in layer III neurons of the mEC, which was not observed in the BC. Moreover, we found that kainate receptor-mediated currents assist in recovery back to the Up state membrane potential following a current-induced hyperpolarisation of individual cells in the mEC. Finally, we were able to generate Up state activity in a network model of exponential integrate-and-fire neurons only supported by AMPA and kainate receptor-mediated currents. We propose that synaptic kainate receptors are responsible for the unique properties of mEC Up states.We also would like to acknowledge support from the Medical Research Council, UK. R.J.D. is on the Cambridge MB/PhD programme. D.S.B. is supported by the Gates Cambridge Trust. V.M. was supported by a Swiss National Science Foundation Early Postdoc Mobility Fellowship