generalized entropic uncertainty relations a new class of uncertainty relations is derived for pairs of observables in a finite dimensional hilbert space which do not have any common eigenvector this class contains an entropic uncertainty relation which improves a previous result of deutsch and confirms a recent conjecture by kraus some comments are made on the extension of these relations to the case where the hilbert space is infinite dimensional

unified approach to classical speed limit and thermodynamic uncertainty relation the total entropy production quantifies the extent of irreversibility in thermodynamic systems which is nonnegative for any feasible dynamics when additional information such as the initial and final states or moments of an observable is available it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes for a particular case we show that our universal relation reduces to a classical speed limit imposing a constraint on the speed of the system s evolution in terms of the hatano sasa entropy production notably the obtained classical speed limit is tighter than the previously reported bound by a constant factor moreover we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation our uncertainty relation holds for systems with time reversal symmetry breaking and recovers several existing bounds our approach provides a unified perspective on two closely related classes of inequality classical speed limits and thermodynamic uncertainty relations

quantum fluctuation relations for the lindblad master equation an open quantum system interacting with its environment can be modeled under suitable assumptions as a markov process described by a lindblad master equation in this work we derive a general set of fluctuation relations for systems governed by a lindblad equation these identities provide quantum versions of jarzynski hatano sasa and crooks relations in the linear response regime these fluctuation relations yield a fluctuation dissipation theorem fdt valid for a stationary state arbitrarily far from equilibrium for a closed system this fdt reduces to the celebrated callen welton kubo formula

universal property of the housekeeping entropy production the entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative the housekeeping entropy production which is a part of total entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state we derive a langevin type stochastic differential equation for the housekeeping entropy production the equation allows us to define a housekeeping entropic time ensuremath tau remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of ensuremath tau is given by the gaussian distribution regardless of system details the gaussian distribution is universal for any systems whether in the steady state or in the transient state and whether they are driven by time independent or time dependent driving forces we demonstrate the universal distribution numerically for model systems

a branch and bound approach to correspondence and grouping problems data correspondence grouping under an unknown parametric model is a fundamental topic in computer vision finding feature correspondences between two images is probably the most popular application of this research field and is the main motivation of our work it is a key ingredient for a wide range of vision tasks including three dimensional reconstruction and object recognition existing feature correspondence methods are based on either local appearance similarity or global geometric consistency or a combination of both in some heuristic manner none of these methods is fully satisfactory especially in the presence of repetitive image textures or mismatches in this paper we present a new algorithm that combines the benefits of both appearance based and geometry based methods and mathematically guarantees a global optimization our algorithm accepts the two sets of features extracted from two images as input and outputs the feature correspondences with the largest number of inliers which verify both the appearance similarity and geometric constraints specifically we formulate the problem as a mixed integer program and solve it efficiently by a series of linear programs via a branch and bound procedure we subsequently generalize our framework in the context of data correspondence grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems our algorithm has been validated successfully on synthesized data and challenging real images

on the existence of quantum subdynamics it is shown using only elementary operator algebra that an open quantum system coupled to its environment will have a subdynamics reduced dynamics as an exact consequence of the reversible dynamics of the composite system only when the states of system and environment are uncorrelated furthermore it is proved that for a finite temperature the kms condition for the lowest order correlation function cannot be reproduced by any type of linear subdynamics except the reversible hamiltonian one of a closed system the first statement can be seen as a particular case of a more general theorem of takesaki on the properties of conditional expectations in von neumann algebras the concept of subdynamics used here allows for memory effects no assumption is made of a markov property for dynamical systems based on commutative algebras of observables the subdynamics always exists as a stochastic process in the random variable defining the open subsystem

a stratified approach for camera calibration using spheres this paper proposes a stratified approach for camera calibration using spheres previous works have exploited epipolar tangents to locate frontier points on spheres for estimating the epipolar geometry it is shown in this paper that other than the frontier points two additional point features can be obtained by considering the bitangent envelopes of a pair of spheres a simple method for locating the images of such point features and the sphere centers is presented an algorithm for recovering the fundamental matrix in a plane plus parallax representation using these recovered image points and the epipolar tangents from three spheres is developed a new formulation of the absolute dual quadric as a cone tangent to a dual sphere with the plane at infinity being its vertex is derived this allows the recovery of the absolute dual quadric which is used to upgrade the weak calibration to a full calibration experimental results on both synthetic and real data are presented which demonstrate the feasibility and the high precision achieved by our proposed algorithm

fluctuation theorems work is not an observable the characteristic function of the work performed by an external time dependent force on a hamiltonian quantum system is identified with the time ordered correlation function of the exponentiated system s hamiltonian a similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the jarzynski work theorem

the tasaki crooks quantum fluctuation theorem starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in talkner et al 2007 phys rev e 75 050102 preprint cond mat 0703213 the quantum version of the crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse fourier transformation

general entropy like uncertainty relations in finite dimensions we revisit entropic formulations of the uncertainty principle up for an arbitrary pair of positive operator valued measures povm a and b acting on finite dimensional hilbert space salicr generalized entropies including r nyi and tsallis ones among others are used as uncertainty measures associated with the distribution probabilities corresponding to the outcomes of the observables we obtain a nontrivial lower bound for the sum of generalized entropies for any pair of entropic functionals which is valid for both pure and mixed states the bound depends on the overlap triplet with ca respectively cb being the overlap between the elements of the povm a respectively b and the overlap between the pair of povm our approach is inspired by that of de vicente and s nchez ruiz 2008 phys rev a 77 042110 and consists in a minimization of the entropy sum subject to the landau pollak inequality that links the maximum probabilities of both observables we solve the constrained optimization problem in a geometrical way and furthermore when dealing with r nyi or tsallis entropic formulations of the up we overcome the h lder conjugacy constraint imposed on the entropic indices by the riesz thorin theorem in the case of nondegenerate observables we show that for given the bound obtained is optimal and that for r nyi entropies our bound improves deutsch one but maassen uffink bound prevails when finally we illustrate by comparing our bound with known previous results in particular cases of r nyi and tsallis entropies

finite time landauer principle we study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time we present a general framework for minimizing the average work required when full control of a system s microstates is possible in addition to exact numerical results we find simple bounds proportional to the variance of the microscopic distribution associated with the state of the bit in the short time limit we get a closed expression for the minimum average amount of work needed to erase a bit the average work associated with the optimal protocol can be up to a factor of 4 smaller relative to protocols constrained to end in local equilibrium assessing prior experimental and numerical results based on heuristic protocols we find that our bounds often dissipate an order of magnitude less energy

unified treatment of the quantum fluctuation theorem and the jarzynski equality in terms of microscopic reversibility there are two related theorems which hold even in far from equilibrium namely fluctuation theorem and jarzynski equality fluctuation theorem states the existence of symmetry of fluctuation of entropy production while the jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes on the other hand the relationship between these theorems was investigated by crooks phys rev e 60 2721 1999 for the classical stochastic systems in this paper we derive quantum analogues of fluctuation theorem and jarzynski equality in terms of microscopic reversibility in other words the quantum analog of the work by crooks is presented also for the quasiclassical langevin system microscopically reversible condition is confirmed

fluctuation theorem for partially masked nonequilibrium dynamics we establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics we introduce a partial entropy production with a subset of all possible transitions and show that the partial entropy production satisfies the integral fluctuation theorem our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines in particular our result gives a unified fluctuation theorem for both autonomous and nonautonomous maxwell s demons where mutual information plays a crucial role furthermore we derive a fluctuation dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations

entropic heisenberg limits and uncertainty relations from the holevo information bound strong and general entropic and geometric heisenberg limits are obtained for estimates of multiparameter unitary displacements in quantum metrology such as the estimation of a magnetic field from the induced rotation of a probe state in three dimensions a key ingredient is the holevo bound on the shannon mutual information of a quantum communication channel this leads to a bayesian bound on performance in terms of the prior distribution of the displacement and the asymmetry of the input probe state with respect to the displacement group a geometric measure of performance related to entropy is proposed for general parameter estimation it is also shown how strong entropic uncertainty relations for mutually unbiased observables such as number and phase position and momentum energy and time and orthogonal spin 1 2 directions can be obtained from elementary applications of holevo s bound a geometric interpretation of results is emphasised in terms of the volumes of quantum and classical statistical ensembles

geometric and algebraic constraints of projected concentric circles and their applications to camera calibration we investigate the projective properties of the feature consisting of two concentric circles we demonstrate there exist geometric and algebraic constraints on its projection we show how these constraints greatly simplify the recoveries of the affine and euclidean structures of a 3d plane as an application we assess the performances of two camera calibration algorithms

efficiency versus speed in quantum heat engines rigorous constraint from lieb robinson bound a long standing open problem whether a heat engine with finite power achieves the carnot efficiency is investgated we rigorously prove a general trade off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines in a first step employing the lieb robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable this inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished using this description we prove an upper bound on efficiency with the aid of quantum information geometry our result generally excludes the possibility of a process with finite speed at the carnot efficiency in quantum heat engines in particular the obtained constraint covers engines evolving with non markovian dynamics which almost all previous studies on this topic fail to address

uncertainty in quantum measurements the object of this letter is to show that except in the case of canonically conjugate observables the generalized heisenberg inequality does not properly express the quantum uncertainty principle it is in general too weak an inequality is obtained which does express the principle

measurement uncertainty relations for discrete observables relative entropy formulation we introduce a new information theoretic formulation of quantum measurement uncertainty relations based on the notion of relative entropy between measurement probabilities in the case of a finite dimensional system and for any approximate joint measurement of two target discrete observables we define the entropic divergence as the maximal total loss of information occurring in the approximation at hand for fixed target observables we study the joint measurements minimizing the entropic divergence and we prove the general properties of its minimum value such a minimum is our uncertainty lower bound the total information lost by replacing the target observables with their optimal approximations evaluated at the worst possible state the bound turns out to be also an entropic incompatibility degree that is a good information theoretic measure of incompatibility indeed it vanishes if and only if the target observables are compatible it is state independent and it enjoys all the invariance properties which are desirable for such a measure in this context we point out the difference between general approximate joint measurements and sequential approximate joint measurements to do this we introduce a separate index for the tradeoff between the error of the first measurement and the disturbance of the second one by exploiting the symmetry properties of the target observables exact values lower bounds and optimal approximations are evaluated in two different concrete examples 1 a couple of spin 1 2 components not necessarily orthogonal 2 two fourier conjugate mutually unbiased bases in prime power dimension finally the entropic incompatibility degree straightforwardly generalizes to the case of many observables still maintaining all its relevant properties we explicitly compute it for three orthogonal spin 1 2 components

self calibration of catadioptric camera with two planar mirrors from silhouettes if an object is interreflected between two planar mirrors we may take an image containing both the object and its multiple reflections i e simultaneously imaging multiple views of an object by a single pinhole camera this paper emphasizes the problem of recovering both the intrinsic and extrinsic parameters of the camera using multiple silhouettes from one single image view pairs among views in a single image can be divided into two kinds by the relationship between the two views in the pair reflected by some mirror real or virtual and in a circular motion epipoles in the first kind of pairs can be easily determined from intersections of common tangent lines of silhouettes based on the projective properties of these epipoles efficient methods are proposed to recover both the imaged circular points and the included angle between two mirrors epipoles in the second kind of pairs can be recovered simultaneously with the projection of intersection line between two mirrors by solving a simple 1d optimization problem using the consistency constraint of epipolar tangent lines fundamental matrices among views in a single image are all recovered using the estimated intrinsic and extrinsic parameters of the camera a euclidean reconstruction can be obtained experiments validate the proposed approach

circular motion geometry using minimal data circular motion or single axis motion is widely used in computer vision and graphics for 3d model acquisition this paper describes a new and simple method for recovering the geometry of uncalibrated circular motion from a minimal set of only two points in four images this problem has been previously solved using nonminimal data either by computing the fundamental matrix and trifocal tensor in three images or by fitting conics to tracked points in five or more images it is first established that two sets of tracked points in different images under circular motion for two distinct space points are related by a homography then we compute a plane homography from a minimal two points in four images after that we show that the unique pair of complex conjugate eigenvectors of this homography are the image of the circular points of the parallel planes of the circular motion subsequently all other motion and structure parameters are computed from this homography in a straightforward manner the experiments on real image sequences demonstrate the simplicity accuracy and robustness of the new method

a new easy camera calibration technique based on circular points inspired by zhang s work a new easy technique for calibrating a camera based on circular points is proposed the proposed technique only requires the camera to observe a newly designed planar calibration pattern referred to as the model plane hereinafter which includes a circle and a pencil of lines passing through the circle s center at a few at least three different unknown orientations then all the five intrinsic parameters can be determined linearly the main point of our new technique is that it needs to know neither metric measurement on the model plane nor the correspondences between points on the model plane and image ones hence it can be done fully automatically the proposed technique is particularly useful for those people who are not familiar with computer vision experiments with simulated data as well as with real images show that our new technique is robust and accurate

extended quantum conditional entropy and quantum uncertainty inequalities quantum states can be subjected to classical measurements whose incompatibility or uncertainty can be quantified by a comparison of certain entropies there is a long history of such entropy inequalities between position and momentum recently these inequalities have been generalized to the tensor product of several hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized our proofs utilize the technique of the original derivation of strong subadditivity of the von neumann entropy

geometric camera calibration using circular control points modern ccd cameras are usually capable of a spatial accuracy greater than 1 50 of the pixel size however such accuracy is not easily attained due to various error sources that can affect the image formation process current calibration methods typically assume that the observations are unbiased the only error is the zero mean independent and identically distributed random noise in the observed image coordinates and the camera model completely explains the mapping between the 3d coordinates and the image coordinates in general these conditions are not met causing the calibration results to be less accurate than expected in the paper a calibration procedure for precise 3d computer vision applications is described it introduces bias correction for circular control points and a nonrecursive method for reversing the distortion model the accuracy analysis is presented and the error sources that can reduce the theoretical accuracy are discussed the tests with synthetic images indicate improvements in the calibration results in limited error conditions in real images the suppression of external error sources becomes a prerequisite for successful calibration

conic reconstruction and correspondence from two views conics are widely accepted as one of the most fundamental image features together with points and line segments the problem of space reconstruction and correspondence of two conics from two views is addressed in this paper it is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views given the relative orientation of the two views these two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics a unified closed form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images

universal trade off relation between power and efficiency for heat engines for a general thermodynamic system described as a markov process we prove a general lower bound for dissipation in terms of the square of the heat current thus establishing that nonvanishing current inevitably implies dissipation this leads to a universal trade off relation between efficiency and power with which we rigorously prove that a heat engine with nonvanishing power never attains the carnot efficiency our theory applies to systems arbitrarily far from equilibrium and does not assume any specific symmetry of the model

camera calibration with three noncollinear points under special motions plane based 2d camera calibration is becoming a hot research topic in recent years because of its flexibility however at least four image points are needed in every view to denote the coplanar feature in the 2d camera calibration can we do the camera calibration by using the calibration object that only has three points some 1d camera calibration techniques use the setup of three collinear points with known distances but it is a kind of special conditions of calibration object setup how about the general setup three noncollinear points we propose a new camera calibration algorithm based on the calibration objects with three noncollinear points experiments with simulated data and real images are carried out to verify the theoretical correctness and numerical robustness of our results because the objects with three noncollinear points have special properties in camera calibration they are midway between 1d and 2d calibration objects our method is actually a new kind of camera calibration algorithm

speed limit for classical stochastic processes we consider the speed limit for classical stochastic markov processes with and without the local detailed balance condition we find that for both cases a trade off inequality exists between the speed of the state transformation and the entropy production the dynamical activity is related to a time scale and plays a crucial role in the inequality for the dynamics without the local detailed balance condition we use the hatano sasa entropy production instead of the standard entropy production our inequalities consist of the quantities that are commonly used in stochastic thermodynamics and explicitly show underlying physical mechanisms

uncertainty relation for smooth entropies uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted while established uncertainty relations apply to cases where the predictions are based on purely classical data e g a description of the system s state before measurement an extended relation which remains valid in the presence of quantum information has been proposed recently berta et al nature phys 6 659 2010 here we generalize this uncertainty relation to one formulated in terms of smooth entropies since these entropies measure operational quantities such as extractable secret key length our uncertainty relation is of immediate practical use to illustrate this we show that it directly implies security of quantum key distribution protocols our security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model

trajectory triangulation 3d reconstruction of moving points from a monocular image sequence we consider the problem of reconstructing the 3d coordinates of a moving point seen from a monocular moving camera i e to reconstruct moving objects from line of sight measurements only the task is feasible only when some constraints are placed on the shape of the trajectory of the moving point we coin the family of such tasks as trajectory triangulation we investigate the solutions for points moving along a straight line and along conic section trajectories we show that if the point is moving along a straight line then the parameters of the line and hence the 3d position of the point at each time instant can be uniquely recovered and by linear methods from at least five views for the case of conic shaped trajectory we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type like a circle in 3d euclidean space for which seven views are sufficient the paradigm of trajectory triangulation in general pushes the envelope of processing dynamic scenes forward thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects where an object could be a single point

the smooth entropy formalism for von neumann algebras we discuss information theoretic concepts on infinite dimensional quantum systems in particular we lift the smooth entropy formalism as introduced by renner and collaborators for finite dimensional systems to von neumann algebras for the smooth conditional min and max entropy we recover similar characterizing properties and information theoretic operational interpretations as in the finite dimensional case we generalize the entropic uncertainty relation with quantum side information of tomamichel and renner and discuss applications to quantum cryptography in particular we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von neumann algebra

fundamental relation between entropy production and heat current we investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical markov processes we establish the fact that quick energy exchange inevitably induces large entropy production in a quantitative form more specifically we prove two inequalities on instantaneous quantities one is applicable to general markov processes induced by heat baths and the other is applicable only to systems with the local detailed balance condition but is stronger than the former one we demonstrate the physical meaning of our result by applying to some specific setups in particular we show that our inequality is tight in the linear response regime

the maximum speed of dynamical evolution abstract we discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time its maximum speed of dynamical evolution previous analyses have given bounds in terms of e the standard deviation of the energy of the system here we give a strict bound that depends only on e e0 the system s average energy minus its ground state energy we also discuss bounds on information processing rates implied by our bound on the speed of dynamical evolution for example adding 1 j of energy to a given computer can never increase its processing rate by more than about 3 1033 operations per second

there is no quantum regression theorem the onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium it is here asserted that this hypothesis fails in the quantum case this is shown first by explicit calculation for the example of quantum brownian motion of an oscillator and then in general from the fluctuation dissipation theorem it is asserted that the correct generalization of the onsager hypothesis is the fluctuation dissipation theorem s0031 9007 96 00679 5

derivation of quantum work equalities using a quantum feynman kac formula on the basis of a quantum mechanical analog of the famous feynman kac formula we present a method to derive nonequilibrium work equalities for isolated quantum systems which include the jarzynski equality and bochkov kuzovlev equality compared with other methods in the literature our method shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems

a flexible new technique for camera calibration we propose a flexible technique to easily calibrate a camera it only requires the camera to observe a planar pattern shown at a few at least two different orientations either the camera or the planar pattern can be freely moved the motion need not be known radial lens distortion is modeled the proposed procedure consists of a closed form solution followed by a nonlinear refinement based on the maximum likelihood criterion both computer simulation and real data have been used to test the proposed technique and very good results have been obtained compared with classical techniques which use expensive equipment such as two or three orthogonal planes the proposed technique is easy to use and flexible it advances 3d computer vision one more step from laboratory environments to real world use

reduced dynamics need not be completely positive the reduced dynamics of a quantum system in contact with a reservoir is generally thought to be completely positive this is certainly true if product initial conditions are used to define the dynamics we show that with correlated initial conditions it need not be so in this case the dynamics can properly be defined only on a subset of initial system states extension by linearity to all possible initial states is trivially possible but the extension may not be physically realizable and may not even be positive let alone completely positive

geometric interpretations of the relation between the image of the absolute conic and sphere images a spherical object has been introduced into camera calibration for several years through utilizing the properties of an image conic which is the projection of the occluding contour of a sphere in the perspective image however in literature only an algebraic interpretation was presented for the relation between the image of the absolute conic and sphere images in this paper we propose two geometric interpretations of this relation and two novel camera calibration methods using sphere images are derived from these geometric interpretations