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This study aims at investigating flexible and transparent thermoplastic polyurethane (TPU) as a novel material for triboelectric nanogenerator (TENG) devices with a polyethylene terephthalate layer. Devices having TPU—either as a flat film or as electrospun micrometer-dimension fibers with varying concentrations of TPU—were tested. The best output performing device provided 21.4 V and 23 μA as open-circuit voltage and short-circuit current respectively, with the application of a small force of 0.33 N indicating the high efficiency of the device. Devices with flat films-obtained using the doctor-blade (DB) technique—have high transparency (80%) as well as high TENG output. The topography of the TPU layer, characterized by atomic force microscopy, reveals nanoscale roughness of the film surface. Finally, we demonstrate that gentle hand tapping on the TENG device can power upto 11 light-emitting diodes (LEDs). The high transparency, lightweight, simple fabrication, flexibility, and robust features of such device make it an added value for various optoelectronic applications.

We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit in the framework of stochastic processes. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance., Comment: Discussions about the tightness and the application of the bound are added. References are updated. 7+10 pages, 3+1 figures

We consider in what sense quantum tunneling is associated with nonclassical probabilistic behavior. We use the Wigner function quasiprobability picture. We give a definition of tunneling that allows us to say whether in a given scenario there is tunneling or not. We prove that this can only happen if the Wigner function is negative and/or a certain measurement operator which we call the tunneling rate operator has a negative Wigner function. We also investigate tunneling in postquantum theories.

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories., Authors' accepted manuscript for inclusion in the Foundations of Physics topical collection on Foundational Aspects of Quantum Information

Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein-Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of $0$ mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.

The ability of quantum devices to preserve or distribute entanglement is essential in employing quantum technologies. Such ability is described and guaranteed by the nonentanglement-breaking (nonEB) feature of participating quantum channels. For quantum information applications relying on entanglement, the certification of the nonEB feature is thus indispensable in designing, testing, and benchmarking quantum devices. Here, we develop a direct and operational approach for the certification of nonEB quantum channels. By utilizing the prepare-and-measure test, we derive a necessary and sufficient condition for witnessing nonEB channels, which is applicable in almost all experimental scenarios. The approach not only unifies and simplifies existing methods in the standard scenario and the measurement-device-independent scenario, but also goes further allowing for certifying the nonEB feature in the semi-device-independent scenario., 14 pages, comments are welcomed. Added references and proofs

The performance of a neural network (NN) for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This includes networks with binary weights, an important class of networks due to their practical hardware implementations. We therefore suggest an alternative approach to training binary NNs. It utilizes a quantum superposition of weight configurations. We show that the quantum training guarantees with high probability convergence towards the globally optimal set of network parameters. This resolves two prominent issues of classical training: (1) the vanishing gradient problem and (2) common convergence to sub-optimal network parameters. We prove that a solution is found after approximately 4 n 2 log n δ N ˜ calls to a comparing oracle, where δ represents a precision, n is the number of training inputs and N ˜ is the number of weight configurations. We give the explicit algorithm and implement it in numerical simulations.

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states., 28 pages, comments welcome

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Renyi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics., Comment: 8 pages. Close to published version

Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics. © IOP Publishing and Deutsche Physikalische Gesellschaft.

A collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory. This is an introduction to those papers, from the perspective of the author. Many of the results may be viewed as a quantification of how much work a generalized Maxwell’s daemon can extract as a function of its extra information. These expressions do not in general involve the Shannon/von Neumann entropy but rather quantities from single-shot information theory. In a limit of large systems composed of many identical and independent parts the Shannon/von Neumann entropy is recovered.

We demonstrate with an experiment how molecules are a natural test-bed for probing fundamental quantum thermodynamics. Single-molecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. By considering the time-resolved emission spectrum of organic molecules as arising from quantum jumps between states, we demonstrate that the quantum Jarzynski equality is satisfied in this set-up. This relates the heat dissipated into the environment to the free energy difference between the initial and final state. We demonstrate also how utilizing the quantum Jarzynski equality allows for the detection of energy shifts within a molecule, beyond the relative shift., 6 pages, 5 figures

It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quantum subspaces. The formula is exact and simple, only containing the number of degrees of freedom and the information capacity of the respective systems. It allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory. The proof of the formula generalizes several randomization notions to general probabilistic theories. This includes a generalization of purity, contributing to the recent effort of finding appropriate generalized entropy measures., Comment: 35 pages, 5 figures, (only change for v2 is that 2 references were updated)

We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as `micro-canonical' and `canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n-mode pure Gaussian states (as quantified by the entropy of a subsystem). We rigorously prove the "concentration of measure" around a finite average, occurring for the entanglement in the thermodynamical limit in both the canonical and the micro-canonical approach. For finite n, we determine analytically the average and standard deviation of the entanglement (as quantified by the reduced purity) between one mode and all the other modes. Furthermore, we numerically investigate more general situations, clearly showing that the onset of the concentration of measure already occurs at relatively small n., Comment: 24 pages, 5 figures, IOP style; conclusions extended, minor layout adjustment

We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal. In previous work we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within $O(N^3)$ steps, where $N$ is the total number of qubits. Here we provide a detailed and more pedagogical proof. We demonstrate that one can use the so-called stabilizer gates to simulate this process efficiently on a classical computer. Furthermore, we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase: (i) the time when saturation of the maximal entanglement is achieved, (ii) the cut-off moment, when the entanglement probability distribution is practically stationary, and (iii) the moment block entanglement scales exhibits volume scaling. We furthermore investigate the mixed state and multipartite setting. Numerically we find that classical and quantum correlations appear to behave similarly and that there is a well-behaved phase-space flow of entanglement properties towards an equilibrium, We describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description. The results form a bridge between certain abstract results concerning typical (also known as generic) entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions., 32 pages, 11 figures

Maxwell's daemon is a popular personification of a principle connecting information gain and extractable work in thermodynamics. A Szilard Engine is a particular hypothetical realization of Maxwell's daemon, which is able to extract work from a single thermal reservoir by measuring the position of particle(s) within the system. Here we investigate the role of particle statistics in the whole process; namely, how the extractable work changes if instead of classical particles fermions or bosons are used as the working medium. We give a unifying argument for the optimal work in the different cases: the extractable work is determined solely by the information gain of the initial measurement, as measured by the mutual information, regardless of the number and type of particles which constitute the working substance.

The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics. In quantum mechanics, the uncertainty principle is considered a limiting factor forbidding a system from being in a state where all possible measurements have perfectly predictable outcomes. Here, Dahlsten et al. show its positive role as the enabler of non-classical dynamics in an interferometer.

We provide a summary of both seminal and recent results on typical entanglement. By typical values of entanglement, we refer here to values of entanglement quantifiers that (given a reasonable measure on the manifold of states) appear with arbitrarily high probability for quantum systems of sufficiently high dimensionality. We work within the Haar measure framework for discrete quantum variables, where we report on results concerning the average von Neumann and linear entropies as well as arguments implying the typicality of such values in the asymptotic limit. We then proceed to discuss the generation of typical quantum states with random circuitry. Different phases of entanglement, and the connection between typical entanglement and thermodynamics are discussed. We also cover approaches to measures on the non-compact set of Gaussian states of continuous variable quantum systems., Comment: Review paper with two quotes and minimalist figures

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics to classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity., Comment: Authors' accepted manuscript

In a recently published letter [S. W. Kim, T. Sagawa, S. DeLiberato, and M. Ueda, PRL 106, 070401 (2011)] the influence of particle statistics on extractable work in the Szilard engine was discussed. We point out that the expressions given there suggest no work extraction is possible in the low temperature limit if more than two particles are used and thus are not optimal. We argue that the optimal extractable work is in general higher and in particular non-decreasing in the number of particles., To appear in PRL

The origin of black hole entropy and the black hole information problem pro- vide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of gravity and quantum mechanics, quantum theory will be unmodied. Here, we examine the black hole information problem in the context of generalisations of quantum theory. In particular, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We compute the time it takes information to escape a black hole, assuming that information is preserved. We nd that under some very general assumptions, the arguments of Page (that information should escape the black hole after half the Hawking photons have been emitted), and the black- hole mirror result of Hayden and Preskill (that information can escape quickly) need to be modied. The modication is determined entirely by what we call the Wootters-Hardy pa- rameter associated with a theory. We nd that although the information leaves the black hole after enough photons have been emitted, it is fairly generic that it fails to appear outside the black hole at this point | something impossible in quantum theory due to the no-hiding theorem. The information is neither inside the black hole, nor outside it, but is delocalised. Our central technical result is an information decoupling theorem which holds in the generalised probabilistic framework.

The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the data processing inequality (DPI). More specifically, we consider arbitrary convex probabilistic theories. These can be equipped with an entropy measure that naturally generalizes the von Neumann entropy, as shown recently in Short and Wehner (2010 New J. Phys. 12 033023) and Barnum et al (2010 New J. Phys. 12 033024). We prove that if the DPI holds with respect to this generalized entropy measure then the underlying theory necessarily respects Tsirelson's bound. We, moreover, generalize this statement to any entropy measure satisfying certain minimal requirements. A consequence of our result is that not all the entropic relations used for deriving Tsirelson's bound via information causality in Pawlowski et al (2009 Nature 461 1101–4) are necessary., New Journal of Physics, 14, ISSN:1367-2630

The lack of knowledge that an observer has about a system limits the amount of work it can extract. This lack of knowledge is normally quantified using the Gibbs/von Neumann entropy. We show that this standard approach is, surprisingly, only correct in very specific circumstances. In general, one should use the recently developed smooth entropy approach. For many common physical situations, including large but internally correlated systems, the resulting values for the extractable work can deviate arbitrarily from those suggested by the standard approach., New Journal of Physics, 13, ISSN:1367-2630

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)., Added clarification on non-cyclic erasure and reversible computation (Appendix E). For a new version of all technical proofs see the Supplementary Information of the journal version (free access)

A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-local, and it is natural to ask whether there are compelling reasons for rejecting theories in which stronger violations are possible. To shed light on this question, we consider post-quantum theories in which maximally non-local states (non-local boxes) occur. It has previously been conjectured that the set of dynamical transformations possible in such theories is severely limited. We settle the question affirmatively in the case of reversible dynamics, by completely characterizing all such transformations allowed in this setting. We find that the dynamical group is trivial, in the sense that it is generated solely by local operations and permutations of systems. In particular, no correlations can ever be created; non-local boxes cannot be prepared from product states (in other words, no analogues of entangling unitary operations exist), and classical computers can efficiently simulate all such processes., 4+3 pages, 1 figure, minor notational changes to match published version

Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The input state is entangled with the weighted graph state and a random circuit is implemented when the experimenter performs local measurements in one fixed basis only. The scheme uses no classical random numbers and is a new and natural application of weighted graph states, Comment: 8 pages, 5 figures

We introduce a "microcanonical" measure (complying with the "general canonical principle") over the second moments of pure bosonic Gaussian states under an energy constraint. We determine the average fidelity for the teleportation of states distributed according to such a measure and compare it to a threshold obtained from a feasible classical strategy. Furthermore, we show that, under the proposed measure, the distribution of the entanglement concentrates around a finite value at the thermodynamical limit and, in general, the typical entanglement of Gaussian states with maximal energy E is not close to the maximum allowed by E., 4 pages + 1 figure (not included in journal version)

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorisation determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorisation governs which evolutions can be realized via thermal interactions, whereas the nondecrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory., Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation, same main results / added minor result on pure bipartite state entanglement (appendix G) / near to published version