Search

This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the optimization of relative entropy for quantum states [Kossmann and Schwonnek, arXiv:2404.17016], we introduce a discretized linearization of the integral representation for the relative entropy for states, enabling us to handle maximization tasks of the relative entropy of a channel over input states. Our approach here extends previous work on minimizing relative entropy to the more complicated domain of maximization. It also provides efficiently computable upper and lower bounds that sandwich the true value with any desired precision, leading to a practical method for computing the relative entropy of channels., Comment: 13 pages

Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase estimation and hybrid quantum-classical optimizers involving parameterized quantum circuits, the latter falling under the umbrella of the variational quantum eigensolver. Here, we analyze the performance of quantum Boltzmann machines for this task, which is a less explored ansatz based on parameterized thermal states and which is not known to suffer from the barren-plateau problem. We delineate a hybrid quantum-classical algorithm for this task and rigorously prove that it converges to an $\varepsilon$-approximate stationary point of the energy function optimized over parameter space, while using a number of parameterized-thermal-state samples that is polynomial in $\varepsilon^{-1}$, the number of parameters, and the norm of the Hamiltonian being optimized. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction that combines classical sampling, Hamiltonian simulation, and the Hadamard test, thus overcoming a key obstacle to quantum Boltzmann machine learning that has been left open since [Amin \textit{et al.}, Phys.~Rev.~X \textbf{8}, 021050 (2018)]. Additionally supporting our main claims are calculations of the gradient and Hessian of the energy function, as well as an upper bound on the matrix elements of the latter that is used in the convergence analysis., Comment: 7 pages, 1 figure, Supplementary material available as 'Ancillary Files'

The precision measurement of the tritium $\beta$-decay spectrum performed by the KATRIN experiment provides a unique way to search for general neutrino interactions (GNI). All theoretical allowed GNI terms involving neutrinos are incorporated into a low-energy effective field theory, and can be identified by specific signatures in the measured tritium $\beta$-spectrum. In this paper an effective description of the impact of GNI on the $\beta$-spectrum is formulated and the first constraints on the effective GNI parameters are derived based on the 4 Mio. electrons collected in the second measurement campaign of KATRIN in 2019. In addition, constraints on selected types of interactions are investigated, thereby exploring the potential of KATRIN to search for more specific new physics cases, including a right-handed W boson, a charged Higgs or leptoquarks.

The projected sensitivity of the effective electron neutrino-mass measurement with the KATRIN experiment is below 0.3 eV (90 % CL) after five years of data acquisition. The sensitivity is affected by the increased rate of the background electrons from KATRIN's main spectrometer. A special shifted-analysing-plane (SAP) configuration was developed to reduce this background by a factor of two. The complex layout of electromagnetic fields in the SAP configuration requires a robust method of estimating these fields. We present in this paper a dedicated calibration measurement of the fields using conversion electrons of gaseous $^\mathrm{83m}$Kr, which enables the neutrino-mass measurements in the SAP configuration., Comment: 19 pages, 11 figures

Quantum networks consist of various quantum technologies, spread across vast distances, and involve various users at the same time. Certifying the functioning and efficiency of the individual components is a task that is well studied and widely used. However, the power of quantum networks can only be realized by integrating all the required quantum technologies and platforms across a large number of users. In this work, we demonstrate how to certify the distillable entanglement available in multipartite states produced by quantum networks, without relying on the physical realization of its constituent components. We do so by using the paradigm of device independence., Comment: v2: 13 pages, 1 figure

In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning applications, and certain asymmetric quantum states are known to be resourceful in various applications. Symmetry testing algorithms provide a means to identify and quantify these properties with respect to a representation of a group. In this paper, we present a collection of quantum algorithms that realize projections onto the symmetric subspace, as well as the asymmetric subspace, of quantum systems. We describe how this can be modified to realize an antisymmetric projection as well, and we show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit. Using these constructions, we demonstrate applications such as testing for Werner-state symmetry and estimating Schmidt ranks of bipartite states, supported by experimental data from IBM Quantum systems. This work underscores the pivotal role of symmetry in simplifying quantum calculations and advancing quantum information tasks., Comment: 19 pages, 17 figures

Quantum communication relies on the existence of high quality quantum channels to exchange information. In practice, however, all communication links are affected by noise from the environment. Here we investigate the ability of quantum channels to perform quantum communication tasks by restricting the participants to use only local operations and one-way classical communication (one-way LOCC) along with the available quantum channel. In particular, a channel can be used to distill a highly entangled state between two parties, which further enables quantum or private communication. In this work, we invoke the framework of superchannels to study the distillation of a resourceful quantum state, such as a maximally entangled state or a private state, using multiple instances of a point-to-point quantum channel. We use the idea of $k$-extendibility to obtain a semidefinite relaxation of the set of one-way LOCC superchannels and define a class of entanglement measures for quantum channels that decrease monotonically under such superchannels; therefore these measures, dubbed collectively the ``unextendible entanglement of a channel'', yield upper bounds on several communication-theoretic quantities of interest in the regimes of resource distillation and zero error. We then generalize the formalism of $k$-extendibility to bipartite superchannels, thus obtaining functions that are monotone under two-extendible superchannels. This allows us to analyze probabilistic distillation of ebits or secret key bits from a bipartite state when using a resourceful quantum channel. Moreover, we propose semidefinite programs to evaluate several of these quantities, providing a computationally feasible method of comparison between quantum channels for resource distillation., Comment: 32+13 pages, 8 figures

Quantum state exclusion is an operational task that has significance in studying foundational questions related to interpreting quantum theory. In such a task, one is given a system whose state is randomly selected from a finite set, and the goal is to identify a state from the set that is not the true state of the system. An error, i.e., an unsuccessful exclusion, occurs if and only if the state identified is the true state. In this paper, we study the optimal error probability of quantum state exclusion and its error exponent -- the rate at which the error probability decays asymptotically -- from an information-theoretic perspective. Our main finding is a single-letter upper bound on the error exponent of state exclusion given by the multivariate log-Euclidean Chernoff divergence, and we prove that this improves upon the best previously known upper bound. We also extend our analysis to the more complicated task of quantum channel exclusion, and we establish a single-letter and efficiently computable upper bound on its error exponent, even assuming the use of adaptive strategies. We derive both upper bounds, for state and channel exclusion, based on one-shot analysis and formulate them as a type of multivariate divergence measure called a barycentric Chernoff divergence. Moreover, our result on channel exclusion has implications in two important special cases. First, for the special case of two hypotheses, our upper bound provides the first known efficiently computable upper bound on the error exponent of symmetric binary channel discrimination. Second, for the special case of classical channels, we show that our upper bound is achievable by a nonadaptive strategy, thus solving the exact error exponent of classical channel exclusion and generalising a similar result on symmetric binary classical channel discrimination., Comment: 44 pages, 1 figure

The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to hybrid quantum-classical strategies with technological requirements far less challenging to implement than required by the most general strategies allowed by quantum mechanics. In this paper, we prove that these measured relative entropies can be calculated efficiently by means of semi-definite programming, by making use of variational formulas for the measured relative entropies of states and semi-definite representations of the weighted geometric mean and the operator connection of the logarithm. Not only do the semi-definite programs output the optimal values of the measured relative entropies of states and channels, but they also provide numerical characterizations of optimal strategies for achieving them, which is of significant practical interest for designing hypothesis testing protocols., Comment: 33 pages

A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as the contraction coefficient of the channel and the divergence. Interestingly, there exist combinations of channels and divergences for which the contraction coefficient is strictly less than one. Furthermore, understanding the contraction coefficient is fundamental for the study of statistical tasks under privacy constraints. To this end, here we establish upper bounds on contraction coefficients for the hockey-stick divergence under privacy constraints, where privacy is quantified with respect to the quantum local differential privacy (QLDP) framework, and we fully characterize the contraction coefficient for the trace distance under privacy constraints. With the machinery developed, we also determine an upper bound on the contraction of both the Bures distance and quantum relative entropy relative to the normalized trace distance, under QLDP constraints. Next, we apply our findings to establish bounds on the sample complexity of quantum hypothesis testing under privacy constraints. Furthermore, we study various scenarios in which the sample complexity bounds are tight, while providing order-optimal quantum channels that achieve those bounds. Lastly, we show how private quantum channels provide fairness and Holevo information stability in quantum learning settings., Comment: 36 pages; See independent work titled "Sample Complexity of Locally Differentially Private Quantum Hypothesis Testing" by Hao-Chung Cheng, Christoph Hirche, and Cambyse Rouz\'e

We present the first successful trapping of single erbium atoms in an array of optical tweezers. Using a single narrow-line optical transition, we achieve deep cooling for direct tweezer loading, pairwise ejection, and continous imaging without additional recoil suppression techniques. Our tweezer wavelength choice enables us to reach the magic trapping condition by tuning the ellipticity of the trapping light. Additionally, we implement an ultrafast high-fidelity fluorescence imaging scheme using a broad transition, allowing time-resolved study of the tweezer population dynamics from many to single atoms during light-assisted collisions. In particular, we extract a pair-ejection rate that qualitatively agrees with the semiclassical predictions by the Gallagher-Pritchard model. This work represents a promising starting point for the exploration of erbium as a powerful resource for quantum simulation in optical tweezers.

The fact that neutrinos carry a non-vanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass bears important relevance from particle physics to cosmology. In this work, we report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium $\beta$-decay close to the kinematic endpoint. Based on the first five neutrino-mass measurement campaigns, we derive a best-fit value of $m_\nu^{2} = {-0.14^{+0.13}_{-0.15}}~\mathrm{eV^2}$, resulting in an upper limit of $m_\nu < {0.45}~\mathrm{eV}$ at 90 % confidence level. With six times the statistics of previous data sets, amounting to 36 million electrons collected in 259 measurement days, a substantial reduction of the background level and improved systematic uncertainties, this result tightens KATRIN's previous bound by a factor of almost two., Comment: 61 pages, 20 figures, 2 tables

The origin of strong sodium absorption, which has been observed for a few nearby Type Ia supernovae (SNe Ia), remains elusive. Here we analyse two high-signal-to-noise, intermediate-resolution VLT/X-shooter spectra at epochs $+$18 and $+$27 days past peak brightness of the strongly lensed and multiply-imaged Type Ia SN 2016geu which exploded at a redshift of $z = 0.4$. We show that SN 2016geu exhibits very strong, multiple Na I and Ca II absorption lines with a large total Na I D restframe equivalent width of 5.2 $\pm$ 0.2 A, among the highest ever detected for a SN Ia and similar to only a handful of nearby SNe Ia with extraordinary large Na I D EWs. The absorption system is time-invariant and extends over a large velocity span $\sim$ 250 km s$^{-1}$. The majority of the absorption is blueshifted relative to the strongest component, while there are both blueshifted and redshifted components relative to the systemic redshift of the galaxy. The column density ratios and widths of the absorption lines indicate that the absorption likely arises from a combination of interstellar dusty molecular clouds and circumgalactic in- and outflowing material, rather than circumstellar matter around the SN., Comment: 12 pages, 6 figures, accepted for publication in ApJ

We propose to measure the weak decay constant $\alpha_-$ for the decay $\Lambda\rightarrow p\pi^-$ using a both circularly and linearly polarized photon beam with the GlueX spectrometer in Hall D. The measurement will take advantage of the fact that a measurement with both linear and circular photon beam polarization results in an over-constrained set of amplitudes which can be fitted to data and used to extract $\alpha_-$ which will be left as a free parameter in the fit. We expect to determine $\alpha_-$ with statistical uncertainties comparable to existing measurements and independent systematic uncertainties. This measurement can be performed alongside GlueX-II running and requires no new hardware or new beam time. The measurement requires that a sufficient fraction of the electron beam polarization be longitudinal in the Hall D tagger., Comment: Submitted to Jefferson Lab PAC52

Matrix geometric means between two positive definite matrices can be defined equivalently from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain optimisation problems. This diversity already suggests the potential for varied applications, as well as acting as a bridge between different domains. Here we devise new quantum subroutines to efficiently prepare quantum unitary operators that embed the standard matrix geometric mean and its generalisations called the weighted matrix geometric mean. This enables the construction of solutions to the algebraic Riccati equation, which is an important class of nonlinear systems of equations that appears in machine learning, optimal control, estimation, and filtering. Using these subroutines, we present a new class of quantum learning algorithms called quantum geometric mean metric learning. This has applications in efficiently finding the best distance measure and solving classification problems in the weakly supervised limit and for anomaly detection, for both classical and quantum problems. We also show how our method can be generalised to a particular p^th-order system of nonlinear equations. These quantum subroutines for matrix geometric means are also useful in other areas of quantum information. For example, we show how to use them in the estimation of geometric Renyi relative entropies and the Uhlmann fidelity by means of the Fuchs-Caves observable. In particular, our quantum algorithms for estimating the Uhlmann and Matsumoto fidelities have optimal dependence on the precision. Finally, we provide a BQP-complete problem based on matrix geometric means that can be solved by our subroutines, thus characterising their computational capability.

The main contribution of our paper is to introduce a number of multivariate quantum fidelities and show that they satisfy several desirable properties that are natural extensions of those of the Uhlmann and Holevo fidelities. We propose three variants that reduce to the average pairwise fidelity for commuting states: average pairwise $z$-fidelities, the multivariate semi-definite programming (SDP) fidelity, and a multivariate fidelity inspired by an existing secrecy measure. The second one is obtained by extending the SDP formulation of the Uhlmann fidelity to more than two states. All three of these variants satisfy the following properties: (i) reduction to multivariate classical fidelities for commuting states, (ii) the data-processing inequality, (iii) invariance under permutations of the states, (iv) its values are in the interval $[0,1]$; they are faithful, that is, their values are equal to one if and only if all the states are equal, and they satisfy orthogonality, that is their values are equal to zero if and only if the states are mutually orthogonal to each other, (v) direct-sum property, (vi) joint concavity, and (vii) uniform continuity bounds under certain conditions. Furthermore, we establish inequalities relating these different variants, indeed clarifying that all these definitions coincide with the average pairwise fidelity for commuting states. Lastly, we introduce another multivariate fidelity called multivariate log-Euclidean fidelity, which is a quantum generalization of the Matusita multivariate fidelity. We also show that it satisfies most of the desirable properties listed above, it is a function of a multivariate log-Euclidean divergence, and has an operational interpretation in terms of quantum hypothesis testing with an arbitrarily varying null hypothesis., Comment: v2: 100 pages, 1 figure; includes additional content on multivariate geometric fidelities and secrecy-based multivariate fidelities

A pure state of fixed Hamming weight is a superposition of computational basis states such that each bitstring in the superposition has the same number of ones. Given a Hilbert space of the form $\mathcal{H} = (\mathbb{C}_2)^{\otimes n}$, or an $n$-qubit system, the identity operator can be decomposed as a sum of projectors onto subspaces of fixed Hamming weight. In this work, we propose several quantum algorithms that realize a coherent Hamming weight projective measurement on an input pure state, meaning that the post-measurement state of the algorithm is the projection of the input state onto the corresponding subspace of fixed Hamming weight. We analyze a depth-width trade-off for the corresponding quantum circuits, allowing for a depth reduction of the circuits at the cost of more control qubits. For an $n$-qubit input, the depth-optimal algorithm uses $O(n)$ control qubits and the corresponding circuit has depth $O(\log (n))$, assuming that we have the ability to perform qubit resets. Furthermore, the proposed algorithm construction uses only one- and two-qubit gates., Comment: 17 pages, 14 figures; see independent and concurrent work of Zi, Nie, Sun at arXiv:2404.06052 and Piroli, Styliaris, Cirac at arXiv:2403.07604. Accepted for publication in Physical Review A

The probabilistic one-way distillable secret key is equal to the largest expected rate at which perfect secret key bits can be probabilistically distilled from a bipartite state by means of local operations and one-way classical communication. Here we define the set of super two-extendible states and prove that an arbitrary state in this set cannot be used for probabilistic one-way secret-key distillation. This broad class of states includes both erased states and all full-rank states. Comparing the probabilistic one-way distillable secret key with the more commonly studied approximate one-way distillable secret key, our results demonstrate an extreme gap between them for many states of interest, with the approximate one-way distillable secret key being much larger. Our findings naturally extend to probabilistic one-way entanglement distillation, with similar conclusions., Comment: 4+8 pages

Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown state. In this paper, we study the sample complexity of QHT, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. By making use of the wealth of knowledge that already exists in the literature on QHT, we characterize the sample complexity of binary QHT in the symmetric and asymmetric settings, and we provide bounds on the sample complexity of multiple QHT. In more detail, we prove that the sample complexity of symmetric binary QHT depends logarithmically on the inverse error probability and inversely on the negative logarithm of the fidelity. As a counterpart of the quantum Stein's lemma, we also find that the sample complexity of asymmetric binary QHT depends logarithmically on the inverse type II error probability and inversely on the quantum relative entropy, provided that the type II error probability is sufficiently small. We then provide lower and upper bounds on the sample complexity of multiple QHT, with it remaining an intriguing open question to improve these bounds. The final part of our paper outlines and reviews how sample complexity of QHT is relevant to a broad swathe of research areas and can enhance understanding of many fundamental concepts, including quantum algorithms for simulation and search, quantum learning and classification, and foundations of quantum mechanics. As such, we view our paper as an invitation to researchers coming from different communities to study and contribute to the problem of sample complexity of QHT, and we outline a number of open directions for future research., Comment: v3: 58 pages, 1 figure, correction to Corollary 10; see independent and concurrent work of Pensia, Jog, Loh at arXiv:2403.16981

In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation is an upper bound on the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Next, we show that the key cost is bounded from below by the regularized relative entropy of entanglement, which implies the irreversibility of the privacy creation-distillation process for a specific class of states. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost and distillable key in the single-shot regime exhibit a yield-cost relation, and basic consequences for quantum devices are also provided., Comment: 34 pages, 6 figures, 1 table

With a view toward addressing the explosive growth in the computational demands of nuclear structure and reactions modeling, we develop a novel quantum algorithm for neutron-nucleus simulations with general potentials, which provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. In particular, the algorithm can now solve for any band-diagonal to full Hamiltonian matrices, as needed to accommodate a general central potential. This includes exponential Gaussian-like potentials and ab initio inter-cluster potentials (optical potentials). The approach can also accommodate the complete form of the chiral effective-field-theory nucleon-nucleon potentials used in ab initio nuclear calculations. We make this potential available for three different qubit encodings, including the one-hot (OHE), binary (BE), and Gray encodings (GE), and we provide a comprehensive analysis of the number of Pauli terms and commuting sets involved. We find that the GE allows for an efficient scaling of the model-space size $N$ (or number of basis states used) and is more resource efficient not only for tridiagonal Hamiltonians, but also for band-diagonal Hamiltonians having bandwidth up to $N$. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity (QC) scheme. We lay out the explicit grouping of Pauli strings and the diagonalizing unitary under the DGC scheme, and we find that it outperforms the QC scheme, at the cost of a more complex diagonalizing unitary. Lastly, we provide first solutions of the neutron-alpha dynamics from quantum simulations suitable for NISQ processors, using an optical potential rooted in first principles, and a study of the bound-state physics in neutron-Carbon systems, along with a comparison of the efficacy of the OHE and GE., Comment: 38 pages, 13 tables, and 18 figures

Dephasing is a prominent noise mechanism that afflicts quantum information carriers, and it is one of the main challenges towards realizing useful quantum computation, communication, and sensing. Here we consider discrimination and estimation of bosonic dephasing channels, when using the most general adaptive strategies allowed by quantum mechanics. We reduce these difficult quantum problems to simple classical ones based on the probability densities defining the bosonic dephasing channels. By doing so, we rigorously establish the optimal performance of various distinguishability and estimation tasks and construct explicit strategies to achieve this performance. To the best of our knowledge, this is the first example of a non-Gaussian bosonic channel for which there are exact solutions for these tasks., Comment: v1: 21 pages, 7 figures

Objective. Achieving appropriate spinopelvic alignment has been shown to be associated with improved clinical symptoms. However, measurement of spinopelvic radiographic parameters is time-intensive and interobserver reliability is a concern. Automated measurement tools have the promise of rapid and consistent measurements, but existing tools are still limited by some degree of manual user-entry requirements. This study presents a novel artificial intelligence (AI) tool called SpinePose that automatically predicts spinopelvic parameters with high accuracy without the need for manual entry. Methods. SpinePose was trained and validated on 761 sagittal whole-spine X-rays to predict sagittal vertical axis (SVA), pelvic tilt (PT), pelvic incidence (PI), sacral slope (SS), lumbar lordosis (LL), T1-pelvic angle (T1PA), and L1-pelvic angle (L1PA). A separate test set of 40 X-rays was labeled by 4 reviewers, including fellowship-trained spine surgeons and a fellowship-trained radiologist with neuroradiology subspecialty certification. Median errors relative to the most senior reviewer were calculated to determine model accuracy on test images. Intraclass correlation coefficients (ICC) were used to assess inter-rater reliability. Results. SpinePose exhibited the following median (interquartile range) parameter errors: SVA: 2.2(2.3)mm, p=0.93; PT: 1.3(1.2){\deg}, p=0.48; SS: 1.7(2.2){\deg}, p=0.64; PI: 2.2(2.1){\deg}, p=0.24; LL: 2.6(4.0){\deg}, p=0.89; T1PA: 1.1(0.9){\deg}, p=0.42; and L1PA: 1.4(1.6){\deg}, p=0.49. Model predictions also exhibited excellent reliability at all parameters (ICC: 0.91-1.0). Conclusions. SpinePose accurately predicted spinopelvic parameters with excellent reliability comparable to fellowship-trained spine surgeons and neuroradiologists. Utilization of predictive AI tools in spinal imaging can substantially aid in patient selection and surgical planning., Comment: 10 pages, 5 figures, to appear in Journal of Neurosurgery: Spine

The paper is concerned with the completeness property of the system of root vectors of a boundary value problem for the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad y= {\rm col}(y_1, y_2), \quad x \in [0,1], $$ $$ B = {\rm diag}(b_1, b_2), \quad b_1 < 0 < b_2, \quad\text{and}\quad Q \in W_1^n[0,1] \otimes \mathbb{C}^{2 \times 2}, $$ subject to general non-regular two-point boundary conditions $C y(0) + D y(1) = 0$. If $b_2 = -b_1 = 1$ this equation is equivalent to the one dimensional Dirac equation. We establish asymptotic expansion of the characteristic determinant of this boundary value problem. This expansion directly yields new completeness result for the system of root vectors of such boundary value problem with non-regular and even degenerate boundary conditions. We also present several explicit completeness results in terms of the values $Q^{(j)}(0)$ and $Q^{(j)}(1)$. In the case of degenerate boundary conditions and analytic $Q(\cdot)$, the criterion of completeness property is established., Comment: 38 pages, 38 references

To curb the initial spread of SARS-CoV-2, many countries relied on nation-wide implementation of non-pharmaceutical intervention measures, resulting in substantial socio-economic impacts. Potentially, subnational implementations might have had less of a societal impact, but comparable epidemiological impact. Here, using the first COVID-19 wave in the Netherlands as a case in point, we address this issue by developing a high-resolution analysis framework that uses a demographically-stratified population and a spatially-explicit, dynamic, individual contact-pattern based epidemiology, calibrated to hospital admissions data and mobility trends extracted from mobile phone signals and Google. We demonstrate how a subnational approach could achieve similar level of epidemiological control in terms of hospital admissions, while some parts of the country could stay open for a longer period. Our framework is exportable to other countries and settings, and may be used to develop policies on subnational approach as a better strategic choice for controlling future epidemics., Comment: 9 pages, 4 figures and Supplementary Information

Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and linear programming (LP) have wide applicability in many domains of computer science, engineering, mathematics, and physics. Here we focus on semi-definite and linear programs for which the dimensions of the variables involved are exponentially large, so that standard classical SDP and LP solvers are not helpful for such large-scale problems. We propose the QSlack and CSlack methods for estimating their optimal values, respectively, which work by 1) introducing slack variables to transform inequality constraints to equality constraints, 2) transforming a constrained optimization to an unconstrained one via the penalty method, and 3) replacing the optimizations over all possible non-negative variables by optimizations over parameterized quantum states and parameterized probability distributions. Under the assumption that the SDP and LP inputs are efficiently measurable observables, it follows that all terms in the resulting objective functions are efficiently estimable by either a quantum computer in the SDP case or a quantum or probabilistic computer in the LP case. Furthermore, by making use of SDP and LP duality theory, we prove that these methods provide a theoretical guarantee that, if one could find global optima of the objective functions, then the resulting values sandwich the true optimal values from both above and below. Finally, we showcase the QSlack and CSlack methods on a variety of example optimization problems and discuss details of our implementation, as well as the resulting performance. We find that our implementations of both the primal and dual for these problems approach the ground truth, typically achieving errors of order $10^{-2}$., Comment: 66 pages, 11 figures

The variational quantum eigensolver (VQE) is a hybrid quantum--classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the reach of classical brute-force simulation, it is important to assess the quality of solutions produced by them. Here we propose a dual variational quantum eigensolver (dual-VQE) that produces a lower-bound estimate of the ground-state energy. As such, VQE and dual-VQE can serve as quality checks on their solutions; in the ideal case, the VQE upper bound and the dual-VQE lower bound form an interval containing the true optimal value of the ground-state energy. The idea behind dual-VQE is to employ semi-definite programming duality to rewrite the ground-state optimization problem as a constrained maximization problem, which itself can be bounded from below by an unconstrained optimization problem to be solved by a variational quantum algorithm. When using a convex combination ansatz in conjunction with a classical generative model, the quantum computational resources needed to evaluate the objective function of dual-VQE are no greater than those needed for that of VQE. We simulated the performance of dual-VQE on the transverse-field Ising model, and found that, for the example considered, while dual-VQE training is slower and noisier than VQE, it approaches the true value with error of order $10^{-2}$., Comment: 8 pages, 1 figure

We consider stellar interferometry in the continuous-variable (CV) quantum information formalism and use the quantum Fisher information (QFI) to characterize the performance of three key strategies: direct interferometry (DI), local heterodyne measurement, and a CV teleportation-based strategy. In the lossless regime, we show that a squeezing parameter of $r\approx 2$ (18 dB) is required to reach $\approx$ 95\% of the QFI achievable with DI; such a squeezing level is beyond what has been achieved experimentally. In the low-loss regime, the CV teleportation strategy becomes inferior to DI, and the performance gap widens as loss increases. Curiously, in the high-loss regime, a small region of loss exists where the CV teleportation strategy slightly outperforms both DI and local heterodyne, representing a transition in the optimal strategy. We describe this advantage as limited because it occurs for a small region of loss, and the magnitude of the advantage is also small. We argue that practical difficulties further impede achieving any quantum advantage, limiting the merits of a CV teleportation-based strategy for stellar interferometry., Comment: 18 pages, 6 figures, codes included. Comments are welcome

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent., Comment: 59 pages, 11 figures, submission to the second journal special issue dedicated to the memory of G\"oran Lindblad, sequel to arXiv:2307.14932

Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP, QMA, QSZK, QIP(2), QIP_EB(2), and QIP, thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes., Comment: 28 pages, 10 figures, 1 table, submission to the journal special issue honoring A. Ravi P. Rau

We present a comprehensive data set of supernova (SN) 2016adj located within the central dust lane of Centaurus A. SN 2016adj is significantly reddened and after correcting the peak apparent $B$-band magnitude ($m_B = 17.48\pm0.05$) for Milky Way reddening and our inferred host-galaxy reddening parameters (i.e., $R_{V}^{host} = 5.7\pm0.7$ and $A_{V}^{host} = 6.3\pm0.2$), we estimate it reached a peak absolute magnitude of $M_B \sim -18$. Detailed inspection of the optical/NIR spectroscopic time-series reveals a carbon-rich SN Ic and not a SN Ib/IIb as previously suggested in the literature. The NIR spectra shows prevalent carbon-monoxide formation occurring already by +41 days past $B$-band maximum, which is $\approx 11$ days earlier than previously reported in the literature for this object. Interestingly around two months past maximum, the NIR spectrum of SN~2016adj begins to exhibit H features, with a +97~d medium resolution spectrum revealing both Paschen and Bracket lines with absorption minima of $\sim 2000$ km/s, full-width-half-maximum emission velocities of $\sim 1000$ km/s, and emission line ratios consistent with a dense emission region. We speculate these attributes are due to circumstellar interaction (CSI) between the rapidly expanding SN ejecta and a H-rich shell of material formed during the pre-SN phase. A bolometric light curve is constructed and a semi-analytical model fit suggests the supernova synthesized 0.5 solar masses of $^{56}$Ni and ejected 4.2 solar masses of material, though these values should be approached with caution given the large uncertainties associated with the adopted reddening parameters, possible CSI contamination, and known light echo emission. Finally, inspection of Hubble Space Telescope archival data yielded no progenitor detection., Comment: Submitted to A&A, comments are welcome

The concept of antidistinguishability of quantum states has been studied to investigate foundational questions in quantum mechanics. It is also called quantum state elimination, because the goal of such a protocol is to guess which state, among finitely many chosen at random, the system is not prepared in (that is, it can be thought of as the first step in a process of elimination). Antidistinguishability has been used to investigate the reality of quantum states, ruling out $\psi$-epistemic ontological models of quantum mechanics [Pusey et al., Nat. Phys., 8(6):475-478, 2012]. Thus, due to the established importance of antidistinguishability in quantum mechanics, exploring it further is warranted. In this paper, we provide a comprehensive study of the optimal error exponent -- the rate at which the optimal error probability vanishes to zero asymptotically -- for classical and quantum antidistinguishability. We derive an exact expression for the optimal error exponent in the classical case and show that it is given by the multivariate classical Chernoff divergence. Our work thus provides this divergence with a meaningful operational interpretation as the optimal error exponent for antidistinguishing a set of probability measures. For the quantum case, we provide several bounds on the optimal error exponent: a lower bound given by the best pairwise Chernoff divergence of the states, a single-letter semi-definite programming upper bound, and lower and upper bounds in terms of minimal and maximal multivariate quantum Chernoff divergences. It remains an open problem to obtain an explicit expression for the optimal error exponent for quantum antidistinguishability., Comment: 48 pages, submission to the journal special issue honoring Mary Beth Ruskai

Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us to simplify calculations and characterize potentially complicated dynamics of the system with relative ease. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. In our present work, we develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers. Our approach estimates asymmetry measures based on the Hilbert--Schmidt distance, which is significantly easier, in a computational sense, than using fidelity as a metric. The method is derived to measure symmetries of states, channels, Lindbladians, and measurements. We apply this method to a number of scenarios involving open quantum systems, including the amplitude damping channel and a spin chain, and we test for symmetries within and outside the finite symmetry group of the Hamiltonian and Lindblad operators., Comment: 47 pages, 11 figures, submission to the second journal special issue dedicated to the memory of G\"oran Lindblad

The single-letter characterisation of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, `inconclusive' measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterisation of postselected capacities in the setting of entanglement assistance as well as the more general nonsignalling assistance, establishing that they are both equal to the channel's projective mutual information -- a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation-based protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel's ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves., Comment: 38 pages, 5 figures, published in International Journal of Quantum Information (IJQI) as part of a special issue dedicated to Alexander S. Holevo on the occasion of his 80th birthday

We present an analysis of Type Ia Supernovae (SNe~Ia) from both the Carnegie Supernova Project~I (CSP-I) and II (CSP-II), and extend the Hubble diagram from the optical to the near-infrared wavelengths ($uBgVriYJH$). We calculate the Hubble constant, $H_0$, using various distance calibrators: Cepheids, Tip of the Red Giant Branch (TRGB), and Surface Brightness Fluctuations (SBF). Combining all methods of calibrations, we derive $\rm H_0=71.76 \pm 0.58 \ (stat) \pm 1.19 \ (sys) \ km \ s^{-1} \ Mpc^{-1}$ from $B$-band, and $\rm H_0=73.22 \pm 0.68 \ (stat) \pm 1.28 \ (sys) \ km \ s^{-1} \ Mpc^{-1}$ from $H$-band. By assigning equal weight to the Cepheid, TRGB, and SBF calibrators, we derive the systematic errors required for consistency in the first rung of the distance ladder, resulting in a systematic error of $1.2\sim 1.3 \rm \ km \ s^{-1} \ Mpc^{-1}$ in $H_0$. As a result, relative to the statistics-only uncertainty, the tension between the late-time $H_0$ we derive by combining the various distance calibrators and the early-time $H_0$ from the Cosmic Microwave Background is reduced. The highest precision in SN~Ia luminosity is found in the $Y$ band ($0.12\pm0.01$ mag), as defined by the intrinsic scatter ($\sigma_{int}$). We revisit SN~Ia Hubble residual-host mass correlations and recover previous results that these correlations do not change significantly between the optical and the near-infrared wavelengths. Finally, SNe~Ia that explode beyond 10 kpc from their host centers exhibit smaller dispersion in their luminosity, confirming our earlier findings. Reduced effect of dust in the outskirt of hosts may be responsible for this effect., Comment: Revised calculations are made. Will be resubmitted to ApJ