A most compendious and facile quantum de Finetti theorem

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's “exponential” approximation by “almost-product” states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems

On exchangeable continuous variable systems

We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation invariance and exchangeability and representing convex combinations of tensor power states. On the level of the respective density operators this leads to necessary criteria for all these properties which become necessary and sufficient for Gaussian states. For these we use the derived results to provide de Finetti-type theorems for various distance measures

Classification of topologically protected gates for local stabilizer codes

Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be implemented by a constant-depth quantum circuit. Such gates have a certain degree of protection since propagation of errors in a constant-depth circuit is limited by a constant size light cone. For the 2D geometry we show that constant-depth circuits can only implement a finite group of encoded gates known as the Clifford group. This implies that topological protection must be "turned off" for at least some steps in the computation in order to achieve universality. For the 3D geometry we show that an encoded gate U is implementable by a constant-depth circuit only if the image of any Pauli operator under conjugation by U belongs to the Clifford group. This class of gates includes some non-Clifford gates such as the \pi/8 rotation. Our classification applies to any stabilizer code with geometrically local stabilizers and sufficiently large code distance.Comment: 6 pages, 2 figure

A de Finetti representation for finite symmetric quantum states

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe

A Reference Model to Support Risk Identification in Cloud Networks

The rising adoption of cloud computing and increasing interconnections among its actors lead to the emergence of network-like structures and new associated risks. A major obstacle for addressing these risks is the lack of transparency concerning the underlying network structure and the dissemination of risks therein. Existing research does not consider the risk perspective in a cloud network’s context. We address this research gap with the construction of a reference model that can display such networks and therefore supports risk identification. We evaluate the reference model through real-world examples and interviews with industry experts and demonstrate its applicability. The model provides a better understanding of cloud networks and causalities between related risks. These insights can be used to develop appropriate risk management strategies in cloud networks. The reference model sets a basis for future risk quantification approaches as well as for the design of (IT) tools for risk analysis

Limitations of local update recovery in stabilizer-GKP codes: a quantum optimal transport approach

Local update recovery seeks to maintain quantum information by applying local correction maps alternating with and compensating for the action of noise. Motivated by recent constructions based on quantum LDPC codes in the finite-dimensional setting, we establish an analytic upper bound on the fault-tolerance threshold for concatenated GKP-stabilizer codes with local update recovery. Our bound applies to noise channels that are tensor products of one-mode beamsplitters with arbitrary environment states, capturing, in particular, photon loss occurring independently in each mode. It shows that for loss rates above a threshold given explicitly as a function of the locality of the recovery maps, encoded information is lost at an exponential rate. This extends an early result by Razborov from discrete to continuous variable (CV) quantum systems. To prove our result, we study a metric on bosonic states akin to the Wasserstein distance between two CV density functions, which we call the bosonic Wasserstein distance. It can be thought of as a CV extension of a quantum Wasserstein distance of order 1 recently introduced by De Palma et al. in the context of qudit systems, in the sense that it captures the notion of locality in a CV setting. We establish several basic properties, including a relation to the trace distance and diameter bounds for states with finite average photon number. We then study its contraction properties under quantum channels, including tensorization, locality and strict contraction under beamsplitter-type noise channels. Due to the simplicity of its formulation, and the established wide applicability of its finite-dimensional counterpart, we believe that the bosonic Wasserstein distance will become a versatile tool in the study of CV quantum systems.Comment: 30 pages, 2 figure

Magnetic Domain Structure of La0.7Sr0.3MnO3 thin-films probed at variable temperature with Scanning Electron Microscopy with Polarization Analysis

The domain configuration of 50 nm thick La0.7SrMnO3 films has been directly investigated using scanning electron microscopy with polarization analysis (SEMPA), with magnetic contrast obtained without the requirement for prior surface preparation. The large scale domain structure reflects a primarily four-fold anisotropy, with a small uniaxial component, consistent with magneto-optic Kerr effect measurements. We also determine the domain transition profile and find it to be in agreement with previous estimates of the domain wall width in this material. The temperature dependence of the image contrast is investigated and compared to superconducting-quantum interference device magnetometry data. A faster decrease in the SEMPA contrast is revealed, which can be explained by the technique's extreme surface sensitivity, allowing us to selectively probe the surface spin polarization which due to the double exchange mechanism exhibits a distinctly different temperature dependence than the bulk magnetization

Investigation on constitutive IKK activity in the axon initial segment

Poster presentation: The transcription factor NF-kappaB plays a central role in the development and maintenance of the central nervous system and its constitutive activation in neurons has been repeatedly reported. Previous work from our laboratories (poster presentation: Compartimentalized NF-kappaB activity in the axon initial segment) had revealed an intriguing clustering of activated IKKalpha/beta and other downstream elements of an activated NF-kappaB cascade (phospho-IkappaBalpha, phospho-p65(Ser536)) in the axon initial segment (AIS). Accumulation of certain voltage-gated sodium channels (Na(v)1.2), M-type potassium channels (KCNQ2) as well as cytoskeletal anchoring proteins (AnkyrinG) characterise the AIS. However, it is not yet clear how AIS-localized IKK gets activated and whether this can be connected to the constitutive activation of NF-kappaB. Long-term blockade of sodium channels with tetrodotoxin, potassium-channels with linopirdine or NMDA-receptors with MK-801 did not elicit any change upon the constitutive activation of the pathway. Strikingly, the occurrence of phosphorylated IkappaBalpha was even unaltered by 24 h of incubation with protein synthesis inhibitors. Others have reported that impairment of NF-kappaB inhibits neuritogenesis. In this line we observed that the early initiation of IkappaBalpha phosphorylation was susceptible to inhibition of IKK in DIV1–2 neurons. We therefore aim to identify the interaction partners of the activated IKK complex in the AIS. Proteomic methods such as co-immunoprecipitation analyses and mass-spectrometry will help us to identify the key players in the initiation of constitutive IKK phosphorylation and activation in neurons

A strong converse for classical channel coding using entangled inputs

A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission.Comment: 9 pages, revte