arXiv subjects
Publications and source records attributed to Malte C. Tichy.
A sum-wise formulation is proposed for the Kaplan-Meier product limit estimator of partially right-censored survival data. The population estimator is expressed as a sum over the individual units' empirical and semi-empirical contributions, for observed and censored failures, respectively. This intuitive decomposition is applied to visualize the different contributions of failed and censored units to the overall population estimator.
Forecast quality should be assessed in the context of what is possible in theory and what is reasonable to expect in practice. Often, one can identify an approximate upper bound to a probabilistic forecast's sharpness, which sets a lower, not necessarily achievable, limit to error metrics. In retail forecasting, a simple, but often unconquerable sharpness limit is given by the Poisson distribution. When evaluating forecasts using traditional metrics such as Mean Absolute Error, it is hard to judge whether a certain achieved value reflects unavoidable Poisson noise or truly indicates an over-dispersed prediction model. Moreover, every evaluation metric suffers from precision scaling: The metric's value is mostly defined by the selling rate and by the resulting rate-dependent Poisson noise, and only secondarily by the forecast quality. Comparing two groups of forecasted products often yields "the slow movers are performing worse than the fast movers" or vice versa, which we call the naïve scaling trap. To distill the intrinsic quality of a forecast, we stratify predictions into buckets of approximately equal predicted values and evaluate metrics separately per bucket. By comparing the achieved value per bucket to benchmarks defined by the theoretical expectation value of the metric, we obtain an intuitive visualization of forecast quality. This representation can be summarized by a single rating that makes forecast quality comparable among different products or even industries. The thereby developed scaling-aware forecast rating is applied to forecasting models used on the M5 competition dataset as well as to real-life forecasts provided by Blue Yonder's Demand Edge for Retail solution for grocery products in Sainsbury's supermarkets in the United Kingdom. The results permit a clear interpretation and high-level understanding of model quality by non-experts.
Assume that a grocery item is sold 1'234 times on a given day. What should an ideal forecast have predicted for such a well-selling item, on average? More generally, when considering a given outcome value, should the empirical average of forecasted expectation values for that outcome ideally match it? Many people will intuitively answer the first question with "1'234, of course", and affirm the second. Perhaps surprisingly, such grouping of data by outcome induces a bias in the evaluation. An evaluation procedure that is aimed at verifying the absence of bias across velocities, when based on such segregation by outcome, therefore fools forecast evaluators and incentivizes forecasters to produce overly exaggerated (extreme) forecasts. Such anticipatory adjustments jeopardize forecast calibration and clearly worsen the forecast quality - this problem was named the "Forecaster's Dilemma" by Lerch et al. in 2017 (Statististical Science 32, 106). As a solution to check for bias across velocities, forecast evaluators should group pairs of forecasts and outcomes by the predicted values, and evaluate empirical mean outcomes per prediction bucket. Within a simple mathematical treatment for the number of items sold in a supermarket, the reader is walked through the dilemma and its circumvention.
An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson. But four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N fermions there are many possible arrangements into composite bosons. The question is: what determines which fermionic arrangement is going to be realized in a given situation and can such arrangement be considered truly bosonic? This work aims to find the answer to the above question. We propose an entanglement-based method to assess bosonic quality of fermionic arrangements and apply it to study how the ground state of the extended one-dimensional Hubbard model changes as the strength of intra-particle interactions increases.
We report experimental studies of the multi-photon quantum interference of a two-mode three-photon entangled Fock state $|2, 1\rangle$ + $|1, 2\rangle$ impinging on a two-port balanced beam splitter. When the distinguishability between the two input paths is increased, we observe a reduction followed by a resurgence of the quantum interference signal. We ascribe this unusual behavior to the competition among contributions from distinct numbers of interfering photons. Our theoretical analysis shows that this phenomenon will occur for any entangled Fock-state input of the form $|N, M\rangle$ + $|M, N\rangle$ where M, N > 0. Our results are an indication that wave-particle duality may give rise to a wide range of, largely unexplored, phenomena in multi-particle interference.
The theory of composite bosons (cobosons) made of two fermions [Phys. Rev. A 71, 034306 (2005), Phys. Rev. Lett. 109, 260403 (2012)] converges to ordinary structureless bosons in the limit of infinitely strong entanglement between the fermionic constituents. For finite entanglement, the annihilation operator $\hat c$ of a composite boson couples the $N$-coboson Fock-state not only to the $(N-1)$-coboson state -- as for ordinary bosons --, but also to a component which is orthogonal to the Fock-state ladder of cobosons. Coupling with states orthogonal to the Fock ladder arises also in dynamical processes of cobosons. Here, with a Gedanken-experiment involving both mode-splitting and collective Hong-Ou-Mandel-like interference, we derive the characteristic physical signature of the states orthogonal to the Fock ladder generated in the splitting process. This allows to extract microscopic properties of many-fermion-wave functions from the collective coboson behavior. We show that consecutive beam-splitter dynamics increases the deviation from the ideal bosonic behavior pattern, which opens up a rigorous approach to the falsification of coboson theory.
We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excellently previous results obtained by means of fixed-node diffusion Monte Carlo methods and the Bogoliubov depletion approximation. This paves the way towards the exploration of the BEC-BCS crossover physics in mixtures of cold Fermi gases with an arbitrary number of fermion pairs as well as the implementation of Hong-Ou-Mandel-like interference experiments proposed within coboson theory.
We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior under pairwise symmetric and anti-symmetric exchange processes. The scalar product of two many-body states with fermionic, bosonic or generalized exchange symmetry becomes the determinant, permanent or immanant of the matrix containing all mutual scalar products of the occupied single-particle states. As a measurable consequence, immanons are shown to obey a partial Pauli principle that forbids the multiple occupation of single-particle states above a certain threshold. The tendency to favor or oppose multiple occupation of single-particle modes, i.e. the degree of bunching, is the determinant, permanent or immanant of a hermitian positive semi-definite matrix. We exploit this identity to devise a Gedankenexperiment that corroborates the permanental dominance conjecture.
Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisingly rich character. Here, we study many-particle interference using three photons. We show that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behaviour in a scattering process, but that a collective phase, the triad phase, plays a role. We are able to explore the full parameter space of three-photon interference by generating heralded single photons and interfering them in a fibre tritter. Using multiple degrees of freedom - temporal delays and polarisation - we isolate three-photon interference from two-photon interference. Our experiment disproves the view that pairwise two-photon distinguishability uniquely determines the degree of non-classical many-particle interference.
We elucidate the relationship between Schrödinger-cat-like macroscopicity and geometric entanglement, and argue that these quantities are not interchangeable. While both properties are lost due to decoherence, we show that macroscopicity is rare in uniform and in so-called random physical ensembles of pure quantum states, despite possibly large geometric entanglement. In contrast, permutation-symmetric pure states feature rather low geometric entanglement and strong and robust macroscopicity.
The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.
Interferometric signals are degraded by decoherence, which encompasses dephasing, mixing and any distinguishing which-path information. These three paradigmatic processes are fundamentally different, but, for coherent, single-photon and $N00N$-states, they degrade interferometric visibility in the very same way, which impedes the diagnosis of the cause for reduced visibility in a single experiment. We introduce a versatile formalism for many-boson interferometry based on double-sided Feynman diagrams, which we apply to a protocol for differential decoherence diagnosis: Twin-Fock states |N,N> with $N \ge 2$ reveal to which extent decoherence is due to path distinguishability or to mixing, while double-Fock superpositions $|N:M> = (|N,M> + |M,N>)/\sqrt{2} $ with $N > M >0$ additionally witness the degree of dephasing. Hence, double-Fock superposition interferometry permits the differential diagnosis of decoherence processes in a single experiment, indispensable for the assessment of interferometers.
The coherence time constitutes one of the most critical parameters that determines whether or not interference is observed in an experiment. For photons, it is traditionally determined by the effective spectral bandwidth of the photon. Here we report on multi-photon interference experiments in which the multi-photon coherence time, defined by the width of the interference signal, depends on the number of interfering photons and on the measurement scheme chosen to detect the particles. A theoretical analysis reveals that all multi-photon interference with more than two particles features this dependence, which can be attributed to higher-order effects in the mutual indistinguishability of the particles. As a striking consequence, a single, well-defined many-particle quantum state can exhibit qualitatively different degrees of interference, depending on the chosen observable. Therefore, optimal sensitivity in many-particle quantum interferometry can only be achieved by choosing a suitable detection scheme.
We develop a scheme to prepare a desired state or subspace in high-dimensional Hilbert-spaces using repeated applications of a single static projection operator onto the desired target and fixed unitary dynamics. Benchmarks against other control schemes, performed on generic Hamiltonians and on Bose-Hubbard systems, establish the competitiveness of the method. As a concrete application of the control of mesoscopic atomic samples in optical lattices we demonstrate the near deterministic preparation of Schrödinger cat states of all atoms residing on either the odd or the even sites.
Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood quantum statistical effects, the coherent superposition of many-particle amplitudes rapidly overburdens classical computing devices - essentially by creating extremely complicated interference patterns, which also challenge experimental resolution. With the advent of controlled many-particle interference experiments, optical set-ups that can efficiently probe many-boson wave functions - baptised BosonSamplers - have therefore been proposed as efficient quantum simulators which outperform any classical computing device, and thereby challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, there remains one crucial problem: How to certify that a given experimental measurement record is an unambiguous result of sampling bosons rather than fermions or distinguishable particles, or of uncontrolled noise? In this contribution, we describe a statistical signature of many-body quantum interference, which can be used as an experimental (and classically computable) benchmark for BosonSampling.
Bosonic bunching occurs within quantum physics and can be mimicked classically by noncontextual hidden-variable models, which excludes this phenomenon as a means to prove stronger-than-quantum contextuality.
Boson-Sampling holds the potential to experimentally falsify the Extended Church Turing thesis. The computational hardness of Boson-Sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson-sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that were proposed as witnesses of Boson-Sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.
A recent work (2014 New J. Phys. 16 013006) claims that nonmonotonic structures found in the many-particle quantum-to-classical transition (2013 Proc. Natl Acad. Sci. USA 110 1227-1231; 2011 Phys. Rev. A 83 062111) are not exclusive to the many-body domain, but they also appear for single-photon as well as for semi-classical systems. We show that these situations, however, do not incorporate any quantum-to-classical transition, which makes the claims unsustainable.