February 2020

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Author:
Marco Fanizza
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See 10.1103/PhysRevResearch.1.033170. 

 
 
 
 
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Author:
Andreas Winter
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The quantum Stein's Lemma gives the asymptotic error for simple i.i.d. hypothesis testing between two states, where the type-I  error is bounded away from 1, and the type-II error is exponentially small. The exponent is given by the quantum relative entropy between the states. The corresponding question for quantum channels (cptp maps) a priori has two answers, depending on whether we allow adaptive strategies to discriminate the channels or not. In a series of recent papers, Berta et al. (1808.01498), Wang/Wilde (1907.06306) and Fang et al. (1909.05826) have solved both questions and shown that the answers are the same: the Stein exponent for asymmetric channel hypothesis testing, i.e. discriminating between n copies of a channel N and n copies of a channel M, using adaptive strategies is given by the amortized channel divergence, and this quantity equals the regularized plain channel divergence, which is the optimal exponent for parallel strategies. The first part relies on a beautiful resource theory, going back to Matsumoto (1010.1030) in the state setting, where the objects are _pairs_ of quantum channels. The second part is surprisingly not operational, but based on chain rule relations for the relative entropy.

 
 
 
 
 
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Author:
Eric Chitambar
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A multiple access channel describes a situation in which multiple senders are trying to forward messages to a single receiver using some communication medium. In this talk we consider scenarios in which this medium consists of just a single classical or quantum particle. In the quantum case, the particle can be prepared in a superposition state thereby allowing for a richer family of encoding strategies. To make the comparison between quantum and classical channels precise, we introduce an operational framework in which all possible encoding strategies are restricted to particle number-preserving operations.  We then apply this resource-theoretic framework to an N-port interferometer experiment in which each party controls a path the particle can traverse.  When used for the purpose of communication, this setup embodies a multiple access channel. The channels built from a single classical particle are found to be characterized in terms of second-order coherences, and every quantum resource state in this theory is shown to generate a channel outside the classical set.  We then introduce a notion of a ``genuine multiple access channel'', in analog to genuine multipartite entanglement, and we show that an N-local channel generated by a quantum particle can simulate a genuine multiple access channel produced by a classical particle.

 
 
Author:
María García Díaz
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Quantum coherence, or the property of systems which are in a superposition of states yielding interference patterns in suitable experiments, is the main hallmark of departure of quantum mechanics from classical physics. Besides its fascinating epistemological implications, quantum coherence also turns out to be a valuable resource for quantum information tasks, and has even been used in the description of fundamental biological processes. This calls for the development of a resource theory which rigorously formalizes the notion of coherence, that further allows both to quantify the coherence present in physical systems and to study its manipulation in order to better leverage it. This thesis intends to make a contribution to the recently built resource theory of coherence in a number of ways. First, we show that coherence, as formalized by its resource theory, is soundly grounded in the physics of interferometers—at least in the context of Strictly Incoherent Operations—and thus embodies its operational foundations. Second, we note that states can be thought of as constant-output channels, and start to generalize the coherence theory of states to that of channels. In particular, we propose several measures of the coherence content of a channel and further compute them when considering two different classes of free operations: Incoherent Operations and the largest set of Maximally Incoherent Operations. Finally, we investigate the question whether coherence can witness some other manifestations of non-classicality (we mean, beyond interference effects). In particular, we analyze the connection of coherence to the non-classicality of quantum stochastic processes both in the Markovian and in the non-Markovian regimes.

 
Author:
Gerardo Adesso
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The recently established resource theory of quantum thermodynamics offers a framework to determine the ultimate possibilities and limitations in the manipulation of quantum states and in the implementation of nanoscale thermal machines. A core endeavour of this programme is to determine under which conditions can a nonequilibrium quantum state be converted into another using thermal operations. Here we settle this question in the important case of Gaussian quantum states and channels. We provide a complete characterisation of Gaussian thermal operations acting on an arbitrary number of bosonic modes, and derive a simple geometric criterion establishing necessary and sufficient conditions for state transformations under such operations in the general single-mode case, encompassing states with nonzero coherence (squeezing) in the energy eigenbasis. Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.

 
 
 
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