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Johan Aberg

Publications and source records attributed to Johan Aberg.

14 recordsLinked to original sources
arXiv2018

Fully quantum fluctuation theorems

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs with the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy, and the control system that implements the dynamic, we here obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir, but the full description of its evolution, including coherences. This approach moreover opens up for generalizations of the concept of fluctuation relations. Here we introduce `conditional' fluctuation relations that are applicable to non-equilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

quant-ph↗
arXiv2017

Semidefinite tests for latent causal structures

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures where all correlations between observed quantities are solely due to the influence from latent variables. We show that each model of this type imposes a certain signature on the observable covariance matrix in terms of a particular decomposition into positive semidefinite components. This signature, and thus the underlying hypothetical latent structure, can be tested in a computationally efficient manner via semidefinite programming. This stands in stark contrast with the algebraic geometric tools required if the full observable probability distribution is taken into account. The semidefinite test is compared with tests based on entropic inequalities.

stat.ML↗
arXiv2014

Catalytic Coherence

Due to conservation of energy we cannot directly turn a quantum system with a definite energy into a superposition of different energies. However, if we have access to an additional resource in terms of a system with a high degree of coherence, as for standard models of laser light, we can overcome this limitation. The question is to what extent coherence gets degraded when utilized. Here it is shown that coherence can be turned into a catalyst, meaning that we can use it repeatedly without ever diminishing its power to enable coherent operations. This finding stands in contrast to the degradation of other quantum resources, and has direct consequences for quantum thermodynamics, as it shows that latent energy that may be locked into superpositions of energy eigenstates can be released catalytically.

quant-ph↗
arXiv2013

Directed quantum communication

We raise the question whether there is a way to characterize the quantum information transport properties of a medium or material. For this analysis the special features of quantum information have to be taken into account. We find that quantum communication over an isotropic medium, as opposed to classical information transfer, requires the transmitter to direct the signal towards the receiver. Furthermore, for large classes of media there is a threshold, in the sense that `sufficiently much' of the signal has to be collected. Therefore, the medium's capacity for quantum communication can be characterized in terms of how the size of the transmitter and receiver has to scale with the transmission distance to maintain quantum information transmission. To demonstrate the applicability of this concept, an n-dimensional spin lattice is considered, yielding a sufficient scaling of d^(n/3) with the distance d.

quant-ph↗
arXiv2012

Truly work-like work extraction

The work content of non-equilibrium systems in relation to a heat bath is often analyzed in terms of expectation values of an underlying random work variable. However, we show that when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se, in which case the extracted energy is unpredictable, thus intuitively more heat-like than work-like. This raises the question of the `truly' work-like energy that can extracted. Here we consider an alternative that corresponds to an essentially fluctuation-free extraction. We show that this quantity can be expressed in terms of a non-equilibrium generalization of the free energy, or equivalently in terms of a one-shot relative entropy measure introduced in information theory.

quant-ph↗
arXiv2011

Min- and Max-Entropy in Infinite Dimensions

We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain information-theoretic operational interpretations, e.g., the min-entropy as maximum achievable quantum correlation, and the max-entropy as decoupling accuracy. We furthermore generalize the smoothed versions of these entropies and prove an infinite-dimensional quantum asymptotic equipartition property. To facilitate these generalizations we show that the min- and max-entropy can be expressed in terms of convergent sequences of finite-dimensional min- and max-entropies, which provides a convenient technique to extend proofs from the finite to the infinite-dimensional setting.

quant-ph↗
arXiv2011

The thermodynamic meaning of negative entropy

Landauer's erasure principle exposes an intrinsic relation between thermodynamics and information theory: the erasure of information stored in a system, S, requires an amount of work proportional to the entropy of that system. This entropy, H(S|O), depends on the information that a given observer, O, has about S, and the work necessary to erase a system may therefore vary for different observers. Here, we consider a general setting where the information held by the observer may be quantum-mechanical, and show that an amount of work proportional to H(S|O) is still sufficient to erase S. Since the entropy H(S|O) can now become negative, erasing a system can result in a net gain of work (and a corresponding cooling of the environment).

quant-ph↗
arXiv2009

Cumulants and the moment algebra: tools for analysing weak measurements

Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.

quant-ph↗
arXiv2007

Generalized spectroscopy; coherence, superposition, and loss

We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We find that loss channels constructed using linear optics form a special subclass. We suggests a generalized spectroscopy where, in analogy with the absorption spectrum, we measure a "coherence loss spectrum" and a "superposition creation spectrum". The theory is illustrated with examples.

quant-ph↗
arXiv2007

Operational approach to the Uhlmann holonomy

We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements.

quant-ph↗
arXiv2006

Quantifying Superposition

Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement measures, but can also be put in a more direct relation to the latter. By a second quantization of the system it is possible to induce superposition measures from entanglement measures. We consider the measures induced from relative entropy of entanglement and entanglement of formation. We furthermore introduce a class of measures with an operational interpretation in terms of interferometry. We consider the superposition measures under the action of subspace preserving and local subspace preserving channels. The theory is illustrated with models of an atom undergoing a relaxation process in a Mach-Zehnder interferometer.

quant-ph↗
arXiv2006

Fidelity and Coherence Measures from Interference

By utilizing single particle interferometry, the fidelity or coherence of a pair of quantum states is identified with their capacity for interference. We consider processes acting on the internal degree of freedom (e.g., spin or polarization) of the interfering particle, preparing it in states ρ_{A} or ρ_{B} in the respective path of the interferometer. The maximal visibility depends on the choice of interferometer, as well as the locality or non-locality of the preparations, but otherwise depends only on the states ρ_{A} and ρ_{B} and not the individual preparation processes themselves. This allows us to define interferometric measures which probe locality and correlation properties of spatially or temporally separated processes, and can be used to differentiate between processes that cannot be distinguished by direct process tomography using only the internal state of the particle.

quant-ph↗
arXiv2006

Operations and single particle interferometry

Interferometry of single particles with internal degrees of freedom is investigated. We discuss the interference patterns obtained when an internal state evolution device is inserted into one or both the paths of the interferometer. The interference pattern obtained is not uniquely determined by the completely positive maps (CPMs) that describe how the devices evolve the internal state of a particle. By using the concept of gluing of CPMs, we investigate the structure of all possible interference patterns obtainable for given trace preserving internal state CPMs. We discuss what can be inferred about the gluing, given a sufficiently rich set of interference experiments. It is shown that the standard interferometric setup is limited in its abilities to distinguish different gluings. A generalized interferometric setup is introduced with the capacity to distinguish all gluings. We also connect to another approach using the well known fact that channels can be realized using a joint unitary evolution of the system and an ancillary system. We deduce the set of all such unitary `representations' and relate the structure of this set to gluings and interference phenomena.

quant-ph↗