- May 06 2015 quant-ph arXiv:1505.00907v1We introduce the notion of \emphpotential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capacities seem to be as hard to compute as their "plain" analogues. We thus study upper bounds on some potential capacities: For the classical capacity, we give an upper bound in terms of the entanglement of formation. To establish a bound for the quantum and private capacity, we first "lift" the channel to a Hadamard channel and then prove that the quantum and private capacity of Hadamard channel is strongly additive, implying that for these channels, potential and plain capacity are equal. Employing these upper bounds we show that if a channel is noisy, however close it is to the noiseless channel, then it cannot be activated into the noiseless channel by any other contextual channel; this conclusion holds for all the three capacities. Although it is of less importance, we also discuss the so-called environment-assisted quantum capacity, because we are able to characterize its "potential" version.
- Mutually unbiased bases (MUB) are interesting for various reasons. The canonical MUB constructed by Ivanović as well as Wootters and Fields have attracted the most attention. Nevertheless, little is known about anything that is unique to this MUB. We show that the canonical MUB in any prime power dimension is uniquely determined by an extremal orbit of the (restricted) Clifford group except in dimension 3, in which case the trophy is taken by a special symmetric informationally complete measurement (SIC), known as the Hesse SIC. Here the extremal orbit is the orbit with the smallest number of pure states. Quite surprisingly, this characterization does not rely on any concept that is even remotely related to bases or unbiasedness. As a corollary, the canonical MUB is the unique minimal 2-design covariant with respect to the Clifford group except in dimension 3. In addition, these MUB provide an infinite family of highly symmetric frames and positive-operator-valued measures (POVMs), which are of independent interest.
- We study a generalization of Kitaev's abelian toric code model defined on CW complexes. In this model qudits are attached to n dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of coboundary and boundary maps in the locally finite cellular cochain complex and the cellular chain complex. We find that the set of energy-minimizing ground states and the types of charges carried by certain localized excitations depends only on the proper homotopy type of the CW complex. As an application we show that the homological product of a CSS code with the infinite toric code has excitations with abelian anyonic statistics.
- May 06 2015 quant-ph arXiv:1505.00982v1Starting from a simple mapping of a generator of local stochastic dynamics to a quantum Hamiltonian, we derive a condition, which allows us to use the quasi-adiabatic evolution and so relate gapped quantum phases with non-equilibrium's. This leads us to a study of invertible matrix product operators. Finally, we present an ansatz for constructing local stochastic dynamics for which the Perron-Frobenius vector has a Matrix Product Representation. Additionally, we get for free that the dynamics satisfy a generalized form of detailed balance.
- May 06 2015 quant-ph arXiv:1505.00833v1We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
- May 06 2015 math.AG arXiv:1505.01145v1
- May 06 2015 q-bio.BM arXiv:1505.01138v1
- May 06 2015 astro-ph.CO arXiv:1505.01132v1
- May 06 2015 cs.CR arXiv:1505.01131v1
- May 06 2015 cs.LO arXiv:1505.01128v1
- May 06 2015 cond-mat.supr-con cond-mat.str-el arXiv:1505.01127v1
- May 06 2015 physics.chem-ph cond-mat.soft arXiv:1505.01126v1
- May 06 2015 astro-ph.GA arXiv:1505.01124v1
- May 06 2015 math.AP arXiv:1505.01122v1
- May 06 2015 cs.DC arXiv:1505.01120v1
- May 06 2015 cond-mat.mes-hall arXiv:1505.01119v1
- May 06 2015 cs.CE arXiv:1505.01118v1
- May 06 2015 math.CO arXiv:1505.01115v1
- May 06 2015 math.DS arXiv:1505.01113v1
- May 06 2015 math.RT arXiv:1505.01112v1
- May 06 2015 cs.NI arXiv:1505.01111v1
- May 06 2015 physics.optics arXiv:1505.01109v1
- May 06 2015 cond-mat.soft arXiv:1505.01108v1
- May 06 2015 hep-lat arXiv:1505.01106v1
- May 06 2015 q-bio.PE arXiv:1505.01105v1
- May 06 2015 physics.flu-dyn arXiv:1505.01101v1
- May 06 2015 math.GT arXiv:1505.01100v1
- May 06 2015 math.GT arXiv:1505.01099v1
- May 06 2015 hep-ph arXiv:1505.01097v1
- May 06 2015 physics.optics arXiv:1505.01096v1
- May 06 2015 cond-mat.mes-hall arXiv:1505.01095v1
- May 06 2015 math.LO arXiv:1505.01094v1
- May 06 2015 astro-ph.HE astro-ph.GA arXiv:1505.01093v1
- May 06 2015 gr-qc arXiv:1505.01092v1
- May 06 2015 nlin.CD arXiv:1505.01090v1