Landauer's Principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of either use thermodynamic reasoning or rely on specific models based arguable assumptions. Here, we aim at a general minimal setup to formulate in precise terms. We provide simple rigorous proof an improved version the Principle, which is formulated terms equality rather than inequality. The quantum statistical mechanics concepts argumentation. From...

We present a technique for the dissipative preparation of highly entangled multiparticle states atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives system from an arbitrary initial state into Greenberger-Horne-Zeilinger state. demonstrate using our steady can be prepared efficiently in time scales polynomially size. Our protocol assumes generic couplings and will thus enable production...

We examine whether renormalization effects can cause Newton's constant to change dramatically with energy, perhaps even reducing the scale of quantum gravity TeV region without introduction extra dimensions. a model that realizes this possibility and describe experimental signatures from production small black holes.

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., tensoring with n copies of themselves. Completely and completely co-positive are trivial examples this kind. show for every ∈ ℕ, there exist non-trivial property two-dimensional Hilbert spaces is no map which holds all n. For higher dimensions, we reduce the existence question such “tensor-stable maps” to a one-parameter family an affirmative answer would imply non-positive partial transpose...

Standard calculations suggest that the entropy of our universe is dominated by black holes, whose order their area in Planck units, although they comprise only a tiny fraction its total energy. Statistical logarithm number microstates consistent with observed macroscopic properties system, hence measure uncertainty about precise state. Therefore, assuming unitarity hole evaporation, standard results largest future quantum state due to Hawking radiation from evaporating holes. However, matter...

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The is induced by convex cones such as sets positive, separable or positive partial transpose operators. It provides bounds on measures for statistical distinguishability states decrease entanglement under protocols involving local operations classical communication other cone-preserving operations. results are formulated terms general base norms lead to contractivity channels, instance,...

We derive upper and lower bounds on the convergence behavior of certain classes one-parameter quantum dynamical semigroups. The we consider consist tensor product channels with commuting Liouvillians. introduce notion Cutoff Phenomenon in setting information theory, show how it exemplifies fact that (quantum) stochastic processes is not solely governed by spectral gap transition map. apply new methods to graph states can be prepared efficiently, albeit constant time, dissipation, give exact...

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can boundary conditions for coupling constant unification, if higher dimensional operators induced by are taken into consideration. We show that generic size of, and uncertainty in, these from be larger than two-loop corrections typically considered group analyses unification. some cases, gravitational modest render unification...

We investigate the microscopic origin of black hole entropy, in particular gap between maximum entropy ordinary matter and that holes. Using curved space, we construct configurations with greater than their area Planck units. These have pathological properties refer to them as monsters. When monsters are excluded recover bound on $S < A^{3/4}$. This implies essentially all microstates a semiclassical associated growth slightly smaller which absorbs some additional energy. Our results...

For a given set of input-output pairs quantum states or observables, we ask the question whether there exists physically implementable transformation that maps each inputs to corresponding output. The physical on are trace-preserving completely positive maps, but also consider variants these requirements. We generalize definition complete positivity linear defined arbitrary subspaces, then formulate this notion as semidefinite program, and relate it by duality approximative extensions map....

We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their difference and dimension underlying space. The inequality is tight sense that equality can be attained for any prescribed value difference, both quantum classical systems. outline implications information theory thermodynamics, such as necessary condition process to close thermodynamic reversibility, or an easily computable channel capacity. Furthermore, we derive upper bound, uniform all...

We propose a simple dark energy model with the following properties: predicts late-time radiation component that is not ruled out by current observational data, but which produces distinctive time-dependent equation of state $w(z)$ for $z<3$. The field can be coupled strongly enough to standard particles detected in colliders, and requires only modest additional particle content little or no fine-tuning other than new scale order milli-electron volts.

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From curved space perspective, they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is curvature or energy density required Planck units, quantum gravitational effects are, conventional effective field theory framework, small everywhere. Since more entropy than a black hole equal mass,...

One of the hallmarks quantum theory is realization that distinct measurements cannot in general be performed simultaneously, stark contrast to classical physics. In this context notions coexistence and joint measurability are employed analyze possibility measuring together two observables, characterizing different degrees compatibility between measurements. It known jointly measurable observables always coexistent, converse holds for various classes including case with outcomes. Here we...

Measurements and feedback are essential in the control of any device operating at quantum scale exploiting features physics. As number components grows, it becomes imperative to consider energetic expense such elementary operations. Here, we derive energy requirements for general measurement, extending previous models obtaining stronger bounds relevant situations, then study two important classes measurements detail. One is projective where obtain exact cost rather than a lower bound, other...

Under the premises that physics is unitary and black hole evaporation complete (no remnants, no topology change), there must exist a one-to-one correspondence between states on future null timelike infinity any earlier spacelike Cauchy surface (e.g., slices preceding formation of hole). We show these requirements exclude large set semiclassical spacetime configurations from Hilbert space quantum gravity. In particular, highest entropy configurations, which account for almost all volume phase...

We investigate the experimental capabilities required to test whether black holes destroy information. show that an experiment capable of illuminating information puzzle must necessarily be able detect or manipulate macroscopic superpositions (i.e., Everett branches). Hence, it could also address fundamental question decoherence versus wave function collapse.

We systematically study the unification of gauge couplings in presence (one or more) effective dimension-5 operators cHGG/4MPl, induced into grand unified theory by gravitational interactions at Planck scale MPl. These alter usual condition for coupling unification, which can, depending on Higgs content H and vacuum expectation value, result scales MX significantly different than naively expected. find non-supersymmetric models SU(5) SO(10) with natural Wilson coefficients c, that easily...

Quantum memories can be regarded as quantum channels that transmit information through time without moving it space. Aiming at a reliable storage of we may thus not only encode the beginning and decode end, but also intervene during transmission - possibility captured by ordinary capacities in Shannon Theory. In this work introduce take into account study them particular for via dynamical semigroups Lindblad form. When evolution is subdivided supplemented additional continuous acting on...

We investigate the problem of quantum searching on a noisy computer. Taking 'fault-ignorant' approach, we analyze algorithms that solve task for various different noise strengths, which are possibly unknown beforehand. prove lower bounds runtime such and thereby find quadratic speedup is necessarily lost (in our models). However, low but constant levels provide (based Grover's algorithm) still outperform best noiseless classical search algorithm.

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement two or more quantum observables. The aim this paper is to provide methods compute optimal type. basic method semidefinite programming, which we apply arbitrary finite collections projective observables a dimensional Hilbert space. quantification based an cost function, assigns penalty getting result $x$ rather than y, for pair (x,y). This induces notion transport probability distributions,...