We propose a quantum generalisation of classical neural network. The neurons are firstly rendered reversible by adding ancillary bits. Then they generalised to being reversible, i.e.\ unitary. (The networks we generalise called feedforward, and have step-function activation functions.) network can be trained efficiently using gradient descent on cost function perform generalisations tasks. demonstrate numerically that it can: (i) compress states onto minimal number qubits, creating...

We report an experimental realization of Maxwell's demon in a photonic setup. show that measurement at the few-photons level followed by feed-forward operation allows extraction work from intense thermal light into electric circuit. The interpretation experiment stimulates derivation equality relating to information acquired measurement. derive bound using this relation and it is agreement with results. Our puts forward systems as platform for experiments related thermodynamics.

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

Abstract We consider the relation between three different approaches to defining quantum states across several times and locations: pseudo-density matrix (PDM), process matrix, multiple-time state approaches. Previous studies have shown that bipartite two-time can reproduce statistics of matrices. Here, we show operational scenarios underlying be represented as PDMs, thereby construct a mapping from matrices with measurements PDMs. The existence this implies PDMs can, like model processes...

We find that generic entanglement is physical, in the sense it can be generated polynomial time from two-qubit gates picked at random. prove as main result such a process generates average of uniform (Haar) measure most $O(N^3)$ steps for $N$ qubits. This despite an exponentially growing number being necessary generating fully on state space. Numerics furthermore show variation cut-off allowing one to associate specific with achievement distribution. Various extensions this work are...

A remarkable feature of quantum theory is non-locality (i.e. the presence correlations which violate Bell inequalities). However, are not maximally non-local, and it natural to ask whether there compelling reasons for rejecting theories in stronger violations possible. To shed light on this question, we consider post-quantum non-local states (non-local boxes) occur. It has previously been conjectured that set dynamical transformations possible such severely limited. We settle question...

We consider how to tell the time-ordering associated with measurement data from quantum experiments at two times and any number of qubits. define an arrow time inference problem. conditions on initial final states that are symmetric or asymmetric under reversal. represent spatiotemporal via pseudodensity matrix space-time state. There is a forward process which completely positive trace-preserving (CPTP) reverse obtained alternative recovery map based inverting unitary dilations. For...

Two approaches to small-scale and quantum thermodynamics are fluctuation relations one-shot statistical mechanics. Fluctuation (such as Crooks' Theorem Jarzynski's Equality) relate nonequilibrium behaviors equilibrium quantities such free energy. One-shot mechanics involves statements about every run of an experiment, not just averages over trials. We investigate the relation between two approaches. show that both feature same notions work probability distributions possible values. The...

The use of the von Neumann entropy in formulating laws thermodynamics has recently been challenged. It is associated with average work whereas guaranteed to be extracted any single run an experiment more interesting quantity general. We show that expression quantifies majorization determines optimal work. argue it should therefore central statistical mechanics, rather than entropy. In limit many identical and independent subsystems (asymptotic i.i.d) expressions are recovered but...

We investigate the entanglement within a system undergoing random, local process. find that there is initially phase of very fast generation and spread entanglement. At end this typically maximal. In Oliveira et al (2007 Phys. Rev. Lett. 98 130502) we proved maximal reached to fixed arbitrary accuracy O(N3) steps, where N total number qubits. Here provide detailed more pedagogical proof. demonstrate one can use so-called stabilizer gates simulate process efficiently on classical computer....

We experimentally probe the interplay of quantum switch with laws thermodynamics. The places two channels in a superposition orders and may be applied to thermalizing channels. Quantum-switching thermal has been shown give apparent violations second law. Central these is how switching can increase capacity communicate information. show this it consistent thermodynamics, demonstrating thermodynamic resources are consumed. use nuclear magnetic resonance approach coherently controlled...

We provide a summary of both seminal and recent results on typical entanglement. By 'typical' values entanglement, we refer here to entanglement quantifiers that (given reasonable measure the manifold states) appear with arbitrarily high probability for quantum systems sufficiently dimensionality. shall focus pure states work within Haar framework discrete variables, where report concerning average von Neumann linear entropies as well arguments implying typicality such in asymptotic limit....

We address a new setting where the second law is under question: thermalizations in quantum superposition of causal orders, enacted by so-called switch. This has been shown to be associated with an increase communication capacity channels, yielding apparent violation data-processing inequality and possibility separate hot from cold. analyze thermodynamics this information increasing process. show how compatible thermodynamics. that there may indeed for consecutive obeying first laws if these...

We design a quantum method for classical information compression that exploits the hidden subgroup algorithm. consider sequence data in database with priori unknown symmetries of type. prove given group structure can be compressed same query complexity as problem, which is exponentially faster than best-known algorithms. moreover algorithm variationally finds and uses it to compress data. There an encoder decoder, along paradigm autoencoders. After training, outputs string description...

Landauer's principle states that it costs at least ${k}_{B}T\mathrm{ln}2$ of work to reset one bit in the presence a heat bath temperature $T$. The bound is achieved unphysical infinite-time limit. Here we ask what possible if restricted finite-time protocols. We prove analytically with cost close finite time. construct an explicit protocol achieves this, which involves thermalizing and changing system's Hamiltonian so as avoid quantum coherences. Using concepts techniques pertaining...

We consider how the energy cost of bit reset scales with time duration protocol. Bit necessarily takes place in finite time, where there is an extra penalty on top quasistatic work derived by Landauer. This dissipated as heat computer, inducing a fundamental limit speed irreversible computers. formulate hardware-independent expression for this framework stochastic processes. derive closed-form lower bound function taken protocol and error. It holds discrete well continuous systems, assuming...

The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that two systems cannot increase under local operations, property known as data processing inequality (DPI). More specifically, we consider arbitrary convex probabilistic theories. These can be equipped with an entropy measure naturally generalizes von Neumann entropy, shown recently in Short Wehner (2010 New J. Phys. 12 033023) Barnum et al 033024)....

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The typically also represents energy observable, Noether-conserved quantity associated with time-invariance law evolution. In both quantum and classical mechanics, demands precise relationship between time observable energy, albeit using slightly different terminology. We distil basic conditions satisfied in including canonical coordinate symmetries inner product invariance. express these framework generalised...

We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. give general operational definitions of energy-related concepts. define energy eigenstates purest stationary states. Planck's constant plays two different roles framework: phase space volume taken up by a pure state and dynamical factor. The is linear combination eigenstates. This allows for Liouville time-evolution equation that applies...