The Quantum Formalization Drive

We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al.

In this short note, I show how a recent result of Alhejji and Smith [arXiv:1909.00787] regarding an optimal uniform continuity bound for classical conditional entropy leads to an optimal uniform continuity bound for quantum conditional entropy of classical--quantum states. The bound is optimal in the sense that there always exists a pair of…

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates subject to various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by {\em single-letter formula} involving a simple optimization over a single use of an…

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement…

We present a continuous-variable quantum key distribution protocol combining a continuous but slightly non-Gaussian modulation together with a efficient reverse reconciliation scheme. We establish the security of this protocol against collective attacks which correspond to a linear quantum channel. In particular, all Gaussian attacks are considered in our…

Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has been recently shown that this universality does not hold in the presence of continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even…

We show that the positivity of the Wigner function of Gaussian states and measurements provides an elegant way to bound the discriminating power of "linear optics", which we formalise as Gaussian measurement operations augmented by classical (feed-forward) communication (GOCC). This allows us to reproduce and generalise the result of Takeoka and Sasaki [PRA…

We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter et al. on finite dimensional density matrices, yields a bound how well a quantum state can be recovered after it has…

We experimentally demonstrate a controlled-phase gate for continuous variables in a fully measurement-based fashion. In our scheme, the two independent input states of the gate, encoded in two optical modes, are teleported into a four-mode Gaussian cluster state. As a result, one of the entanglement links present in the initial cluster state appears in the…

We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models and a uniqueness…

If two separated observers are supplied with entanglement, in the form of $n$ pairs of particles in identical partly-entangled pure states, one member of each pair being given to each observer; they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally-entangled pairs of particles, for example…

A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, coherent classical communication is…

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and to obtain several new conditions. The method is based on a particular approximation of the von Neumann entropy by an…

The class of $μ$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class contains all compact sets as well as many noncompact sets widely used in applications. In this paper we give a characterization of…

A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the…

We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs…