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Entanglement is an essential resource for various quantum-information tasks. When a target system shares entanglement with another memory system and is stored reliably, one can use entanglement at a later time -- this is quantum memory. In practice, entanglement can be exceedingly fragile during a system's evolution. In particular, no entanglement can survive when a so-called entanglement-breaking channel acts on the target system. Are entanglement-breaking channels really useless for maintaining entanglement? As a single channel, this is certainly the case; it cannot be useful for quantum memory. However, in this work, we show that putting together two entanglement-breaking channels in a broadcasting scenario can activate their ability to maintain entanglement -- the channel's quantum memory resource can be super-activated., Comment: 4+3 pages, 2 figures

Informational contributions to thermodynamics can be studied in isolation by considering systems with fully-degenerate Hamiltonians. In this regime, being in non-equilibrium -- termed informational non-equilibrium -- provides thermodynamic resources, such as extractable work, solely from the information content. The usefulness of informational non-equilibrium creates an incentive to obtain more of it, motivating the question of how to concentrate it: can we increase the local informational non-equilibrium of a product state $\rho\otimes\rho$ under a global closed system (unitary) evolution? We fully solve this problem analytically, showing that it is impossible for two-qubits, and it is always possible to find states achieving this in higher dimensions. The notion of bound resources in this framework is then discussed, along with initial global correlations' ability to activate concentration. Finally, we apply our results to study the concentration of purity and intrinsic randomness., Comment: 5+2 pages, 2 figures

Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we propose an extended supporting hyperplane approximation approach for efficiently solving a class of distributionally robust portfolio problems for a general class of additively separable utility functions and polyhedral ambiguity distribution set, applied to a large-scale set of assets. Our technique is validated using a large-scale portfolio of the S&P 500 index constituents, demonstrating robust out-of-sample trading performance. More importantly, our empirical studies show that this approach significantly reduces computational time compared to traditional concave Expected Log-Growth (ELG) optimization, with running times decreasing from several thousand seconds to just a few. This method provides a scalable and practical solution to large-scale robust portfolio optimization, addressing both theoretical and practical challenges., Comment: Submitted to possible publication

The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility -- two physical observables of a single quantum system may not always be measured simultaneously. Apart from being fundamentally important, measurement incompatibility is also a powerful resource in the broad quantum science and technologies, with wide applications to cryptography, communication, random number generation, and device-independent tasks. Since every physical system is unavoidably subject to noise, an important, yet still open, question is how to characterise the ability of noisy quantum dynamics to preserve measurement incompatibility. This work fills this gap by providing the first resource theory of this ability, termed incompatibility preservability. We quantify incompatibility preservability by a robustness measure. Then, we introduce an operational task, entanglement-assisted filter game, to completely characterise both the robustness measure and the conversion of incompatibility preservability. Our results provide a general framework to describe how noisy dynamics affect the uncertainty principle's signature., Comment: 4+5 pages; 4 figures

The Choi-state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi-state can greatly simplify problems. It also offers an alternative approach to the characterisation of a channel, with properties of the Choi-state providing novel insight into a channel's behaviour. The rank of a Choi-state, termed the Choi-rank, has proven to be an important characterising property, and here, its significance is further elucidated through an operational interpretation. The Choi-rank is shown to provide a universal bound on how successfully two agents, Alice and Bob, can perform an entanglement-assisted exclusion task. The task can be considered an extension of super-dense coding, where Bob can only output information about Alice's encoded bit-string with certainty. Conclusive state exclusion, in place of state discrimination, is therefore considered at the culmination of the super-dense coding protocol. In order to prove this result, a necessary condition for conclusive k-state exclusion of a set of states is presented in order to achieve this result, and the notions of weak and strong exclusion are introduced., Comment: 6 + 3 pages, 2 figures

This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which are deterministic and others are stochastic. The decision-maker's cumulative value is updated at each stage, reflecting the outcomes of the chosen alternatives. After formulating this as a stochastic control problem, we delineate the necessary optimality conditions for it. Two illustrative examples from optimal betting and inventory management are provided to support our theory., Comment: submitted for possible publication

We provide a thermodynamic task to certify the general quantum resources of both states and channels via work extraction, showing that general quantum resources provide advantages in work extraction. Such work extraction tasks can be further applied to certify quantum entanglement in a one-sided device-independent way. As an application, we report a novel type of anomalous energy flow -- a type of locally extractable energy that is attributed to the globally distributed entanglement. Finally, we show that the existence of this novel anomalous energy flow is equivalent to measurement incompatibility., Comment: 5+3 pages; 1 figure

We consider a thermodynamic framework to quantify instrument incompatibility via a resource theory subject to thermodynamic constraints. We use the minimal thermalisation time needed to erase incompatibility's signature to measure incompatibility. Unexpectedly, this time value is equivalent to incompatibility advantage in a work extraction task. Hence, both thermalisation time and extractable work can directly quantify instrument incompatibility. Finally, we show that incompatibility signatures must vanish in non-Markovian thermalisation., Comment: 5+15 pages, 3 figures

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the $Z_2$ and $U(1)$ lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the $Z_2$ lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics., Comment: 38 pages, 16 figures, 3 tables, v2: Typo fixed. Additional shot uncertainty discussion and references added

This paper introduces a novel robust trading paradigm, called \textit{multi-double linear policies}, situated within a \textit{generalized} lattice market. Distinctively, our framework departs from most existing robust trading strategies, which are predominantly limited to single or paired assets and typically embed asset correlation within the trading strategy itself, rather than as an inherent characteristic of the market. Our generalized lattice market model incorporates both serially correlated returns and asset correlation through a conditional probabilistic model. In the nominal case, where the parameters of the model are known, we demonstrate that the proposed policies ensure survivability and probabilistic positivity. We then derive an analytic expression for the worst-case expected gain-loss and prove sufficient conditions that the proposed policies can maintain a \textit{positive expected profits}, even within a seemingly nonprofitable symmetric lattice market. When the parameters are unknown and require estimation, we show that the parameter space of the lattice model forms a convex polyhedron, and we present an efficient estimation method using a constrained least-squares method. These theoretical findings are strengthened by extensive empirical studies using data from the top 30 companies within the S\&P 500 index, substantiating the efficacy of the generalized model and the robustness of the proposed policies in sustaining the positive expected profit and providing downside risk protection., Comment: submitted for possible publication

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a novel task which we term $\eta$-unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time. We further show that a special type of measurement complementarity is equivalent to advantages in certain encryption tasks. Finally, our analysis suggest that complementarity of measurement and state ensemble can be interpreted as strong forms of measurement incompatibility and quantum steering, respectively., Comment: 6+5 pages; 4 figures

Steering resources, central for quantum advantages in one-sided device-independent quantum information tasks, can be enhanced via local filters. Recently, reversible steering conversion under local filters has been fully characterised. Here, we solve the problem in the irreversible scenario, which leads to a complete understanding of stochastic steering distillation. This result also provides an operational interpretation of the max-relative entropy as the optimal filter success probability. We further show that all steering measures can be used to quantify measurement incompatibility in certain stochastic steering distillation scenarios. Finally, for a broad class of steering robustness measures, we show that their maximally achievable values in stochastic steering distillation are always upper bounded by different types of incompatibility robustness measures. Hence, measurement incompatibility sets the fundamental limitations for stochastic steering distillation., Comment: 5+4 pages; 2 figures

We show that the incompatibility of a set of measurements cannot be increased by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation. This result holds for several measures of incompatibility, such as those based on robustness and convex weight. Expanding these ideas to Einstein-Podolsky-Rosen steering experiments, we are able to solve the problem of the maximum steerability obtained with respect to the most general local filters in a way that allows for an explicit calculation of the filter operation. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps., Comment: 12 pages, 1 figure, comments welcome

This paper introduces a unified framework for adaptive portfolio management, integrating dynamic Black-Litterman (BL) optimization with the general factor model, Elastic Net regression, and mean-variance portfolio optimization, which allows us to generate investors views and mitigate potential estimation errors systematically. Specifically, we propose an innovative dynamic sliding window algorithm to respond to the constantly changing market conditions. This algorithm allows for the flexible window size adjustment based on market volatility, generating robust estimates for factor modeling, time-varying BL estimations, and optimal portfolio weights. Through extensive ten-year empirical studies using the top 100 capitalized assets in the S&P 500 index, accounting for turnover transaction costs, we demonstrate that this combined approach leads to computational advantages and promising trading performances., Comment: 22 pages, 7 figures

Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other then the maximally mixed state are considered to be in informational non-equilibrium. An important yet still open question is: how to characterise the ability of quantum dynamics to maintain informational non-equilibrium? Here, the dynamical resource theory of informational non-equilibrium preservability is introduced to begin providing an answer to this question. A characterisation of the allowed operations is given for qubit channels and the n dimensional Weyl-covariant channels - a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channels classical capacity and its ability to maintain informational non-equilibrium is made., Comment: 5 + 24 pages, 1 + 3 figures

In this paper, we extend the existing double linear policy by incorporating time-varying weights instead of constant weights and study a certain robustness property, called robust positive expectation (RPE), in a discrete-time setting. We prove that the RPE property holds by employing a novel elementary symmetric polynomials characterization approach and derive an explicit expression for both the expected cumulative gain-loss function and its variance. To validate our theory, we perform extensive Monte Carlo simulations using various weighting functions. Furthermore, we demonstrate how this policy can be effectively incorporated with standard technical analysis techniques, using the moving average as a trading signal., Comment: Submitted for possible publication

This paper extends the existing drawdown modulation control policy to include a novel restart mechanism for trading. It is known that the drawdown modulation policy guarantees the maximum percentage drawdown no larger than a prespecified drawdown limit for all time with probability one. However, when the prespecified limit is approaching in practice, such a modulation policy becomes a stop-loss order, which may miss the profitable follow-up opportunities if any. Motivated by this, we add a data-driven restart mechanism into the drawdown modulation trading system to auto-tune the performance. We find that with the restart mechanism, our policy may achieve a superior trading performance to that without the restart, even with a nonzero transaction costs setting. To support our findings, some empirical studies using equity ETF and cryptocurrency with historical price data are provided.

The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We prove that the frequency-dependent log-optimal portfolio problem with costs is equivalent to a concave program and provide a version of the dominance theorem with costs to determine when an investor should invest all available funds in a particular asset. Then, we show that transaction costs may cause a bankruptcy issue for the frequency-dependent log-optimal portfolio. To address this issue, we approximate the problem to obtain a quadratic concave program and derive necessary and sufficient optimality conditions. Additionally, we prove a version of the two-fund theorem, which states that any convex combination of two optimal weights from the optimality conditions is still optimal. We test our proposed methods using both intraday and daily price data. Finally, we extend our empirical studies to an online trading scenario by implementing a sliding window approach. This approach enables us to solve a sequence of concave programs rather than a potentially computational complex stochastic dynamic programming problem., Comment: Submitted for possible publication

A trading system is said to be {robust} if it generates a robust return regardless of market direction. To this end, a consistently positive expected trading gain is often used as a robustness metric for a trading system. In this paper, we propose a new class of trading policies called the {double linear policy} in an asset trading scenario when the transaction costs are involved. Unlike many existing papers, we first show that the desired robust positive expected gain may disappear when transaction costs are involved. Then we quantify under what conditions the desired positivity can still be preserved. In addition, we conduct heavy Monte-Carlo simulations for an underlying asset whose prices are governed by a geometric Brownian motion with jumps to validate our theory. A more realistic backtesting example involving historical data for cryptocurrency Bitcoin-USD is also studied., Comment: Submitted to for possible publication. arXiv admin note: substantial text overlap with arXiv:2202.02300

In this paper, we propose a data-driven sliding window approach to solve a log-optimal portfolio problem. In contrast to many of the existing papers, this approach leads to a trading strategy with time-varying portfolio weights rather than fixed constant weights. We show, by conducting various empirical studies, that the approach possesses a superior trading performance to the classical log-optimal portfolio in the sense of having a higher cumulative rate of returns., Comment: To appear in the IFAC-PapersOnline (25th International Symposium on Mathematical Theory of Network and Systems)

With thousands of news articles from hundreds of sources distributed and shared every day, news consumption and information acquisition have been increasingly difficult for readers. Additionally, the content of news articles is becoming catchy or even inciting to attract readership, harming the accuracy of news reporting. We present Islander, an online news analyzing system. The system allows users to browse trending topics with articles from multiple sources and perspectives. We define several metrics as proxies for news quality, and develop algorithms for automatic estimation. The quality estimation results are delivered through a web interface to newsreaders for easy access to news and information. The website is publicly available at https://islander.cc/

One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global $n$-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize -- in the sense of providing both the necessary and sufficient conditions -- when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states., Comment: 8+10 pages, 9 figures, 2 tables. Virtually the same as the published version

A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the trader in advance. However, in practice, the return distributions are indeed {ambiguous}; i.e., the true distribution is unknown to the trader or it is partially known at best. To this end, a {distributional robust log-optimal portfolio problem} formulation arises naturally. While the problem formulation takes into account the ambiguity on return distributions, the problem needs not to be tractable in general. To address this, in this paper, we propose a {supporting hyperplane approximation} approach that allows us to reformulate a class of distributional robust log-optimal portfolio problems into a linear program, which can be solved very efficiently. Our framework is flexible enough to allow {transaction costs}, {leverage and shorting}, {survival trades}, and {diversification considerations}. In addition, given an acceptable approximation error, an efficient algorithm for rapidly calculating the optimal number of hyperplanes is provided. Some empirical studies using historical stock price data are also provided to support our theory., Comment: submitted for possible publication

We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility induces a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem -- which implicitly involves some notion of incompatibility -- for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems., Comment: 14+16 pages and 3 figures. New results added and largely rewritten. Accepted for publication in Quantum

The take-off point for this paper is the Simultaneous Long-Short (SLS) control class, which is known to guarantee the so-called robust positive expectation (RPE) property. That is, the expected cumulative trading gain-loss function is guaranteed to be positive for a broad class of stock price processes. This fact attracts many new extensions and ramifications to the SLS theory. However, it is arguable that "systematic" way to select an optimal decision variable that is robust in the RPE sense is still unresolved. To this end, we propose a modified SLS control structure, which we call the {double linear feedback control scheme}, that allows us to solve the issue above for stock price processes involving independent returns. In this paper, we go beyond the existing literature by not only deriving explicit expressions for the expected value and variance of cumulative gain-loss function but also proving various theoretical results regarding {robust positive expected growth} and {monotonicity}. Subsequently, we propose a new {robust optimal gain selection problem} that seeks a solution maximizing the expected trading gain-loss subject to the prespecified standard deviation {and} RPE constraints. Under some mild conditions, we show that the optimal solution exists and is unique. Moreover, a simple graphical approach that allows one to systematically determine the optimal solution is also proposed. Finally, some numerical and empirical studies using historical price data are also provided to support our theory., Comment: Submitted for possible publication

Energy transfer and information transmission are two fundamental aspects of nature. They are seemingly unrelated, while recent findings suggest that a deep connection between them is to be discovered. This amounts to asking: can we phrase the processes of transmitting classical bits equivalently as specific energy-exchanging tasks, thereby uncovering foundational links between them? We answer this question positively by showing that, for a broad class of classical communication tasks, transmitting $n$ bits of classical information via quantum dynamics is equivalent to extracting $n$ units of energy in a thermodynamic work-extraction task. This finding not only provides an analytical correspondence between information transmission and energy extraction tasks but also quantifies classical communication by thermodynamics. In the asymptotic regime, our results further provide thermodynamic meanings for the well-known Holevo-Schumacher-Westmoreland Theorem in quantum communication theory., Comment: 4+16 pages & 3 figures. Largely rewritten with new title and new results

Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples., Comment: 13 pages, 2 figures, comments welcome!

Recent results have demonstrated that samplers constructed with flow-based generative models are a promising new approach for configuration generation in lattice field theory. In this paper, we present a set of methods to construct flow models for targets with multiple separated modes (i.e. theories with multiple vacua). We demonstrate the application of these methods to modeling two-dimensional real scalar field theory in its symmetry-broken phase. In this context we investigate the performance of different flow-based sampling algorithms, including a composite sampling algorithm where flow-based proposals are occasionally augmented by applying updates using traditional algorithms like HMC., Comment: 33 pages, 29 figures

In this paper, we consider a frequency-based portfolio optimization problem with $m \geq 2$ assets when the expected logarithmic growth (ELG) rate of wealth is used as the performance metric. With the aid of the notion called dominant asset, it is known that the optimal ELG level is achieved by investing all available funds on that asset. However, such an "all-in" strategy is arguably too risky to implement in practice. Motivated by this issue, we study the case where the portfolio weights are chosen in a rather ad-hoc manner and a buy-and-hold strategy is subsequently used. Then we show that, if the underlying portfolio contains a dominant asset, buy and hold on that specific asset is asymptotically log-optimal with a sublinear rate of convergence. This result also extends to the scenario where a trader either does not have a probabilistic model for the returns or does not trust a model obtained from historical data. To be more specific, we show that if a market contains a dominant asset, buy and hold a market portfolio involving nonzero weights for each asset is asymptotically log-optimal. Additionally, this paper also includes a conjecture regarding the property called high-frequency maximality. That is, in the absence of transaction costs, high-frequency rebalancing is unbeatable in the ELG sense. Support for the conjecture, involving a lemma for a weak version of the conjecture, is provided. This conjecture, if true, enables us to improve the log-optimality result obtained previously. Finally, a result that indicates a way regarding an issue about when should one to rebalance their portfolio if needed, is also provided. Examples, some involving simulations with historical data, are also provided along the way to illustrate the~theory.

Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling conditions to quantized inputs and outputs and can be understood as a general toolkit to study notions of quantum incompatibility. In fact, they include as special cases channel broadcasting, channel extendibility, measurement compatibility, and state marginal problems. After defining the notion of compatibility between global and local dynamics, we provide a solution to the channel marginal problem that takes the form of a semidefinite program. Using this formulation, we construct channel incompatibility witnesses, discuss their operational interpretation in terms of an advantage for a state-discrimination task, prove a gap between classical and quantum dynamical marginal problems and show that the latter is irreducible to state marginal problems., Comment: 4+11 pages and 1 figure with new results

Machine learning (ML) provides effective means to learn from spectrum data and solve complex tasks involved in wireless communications. Supported by recent advances in computational resources and algorithmic designs, deep learning (DL) has found success in performing various wireless communication tasks such as signal recognition, spectrum sensing and waveform design. However, ML in general and DL in particular have been found vulnerable to manipulations thus giving rise to a field of study called adversarial machine learning (AML). Although AML has been extensively studied in other data domains such as computer vision and natural language processing, research for AML in the wireless communications domain is still in its early stage. This paper presents a comprehensive review of the latest research efforts focused on AML in wireless communications while accounting for the unique characteristics of wireless systems. First, the background of AML attacks on deep neural networks is discussed and a taxonomy of AML attack types is provided. Various methods of generating adversarial examples and attack mechanisms are also described. In addition, an holistic survey of existing research on AML attacks for various wireless communication problems as well as the corresponding defense mechanisms in the wireless domain are presented. Finally, as new attacks and defense techniques are developed, recent research trends and the overarching future outlook for AML for next-generation wireless communications are discussed., Comment: 17 pages, 3 figures

At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide. Given the fact that the pandemic is still threatening health and safety, it is in the urgency to understand the COVID-19 contagion process and know how it might be controlled. With this motivation in mind, in this paper, we consider a version of a stochastic discrete-time Susceptible-Infected-Recovered-Death~(SIRD)-based epidemiological model with two uncertainties: The uncertain rate of infected cases which are undetected or asymptomatic, and the uncertain effectiveness rate of control. Our aim is to study the effect of an epidemic control policy on the uncertain model in a control-theoretic framework. We begin by providing the closed-form solutions of states in the modified SIRD-based model such as infected cases, susceptible cases, recovered cases, and deceased cases. Then, the corresponding expected states and the technical lower and upper bounds for those states are provided as well. Subsequently, we consider two epidemic control problems to be addressed: One is almost sure epidemic control problem and the other average epidemic control problem. Having defined the two problems, our main results are a set of sufficient conditions on a class of linear control policy which assures that the epidemic is "well-controlled"; i.e., both of the infected cases and deceased cases are upper bounded uniformly and the number of infected cases converges to zero asymptotically. Our numerical studies, using the historical COVID-19 contagion data in the United States, suggest that our appealingly simple model and control framework can provide a reasonable epidemic control performance compared to the ongoing pandemic situation., Comment: Submitted to the SIAM Journal on Control and Optimization

Recently, new insights have been obtained by jointly studying communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we analyze the role of dynamical resources in a communication setup, and further apply our analysis to thermodynamics. To start with, we study classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. We show that the one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its one-shot classical capacity. When the channel is coherence non-generating, the upper bound is given by a sum of coherence preservability and the bath size of the channel's incoherent version. In this sense, bath sizes can be interpreted as the thermodynamic cost of transmitting classical information. This finding provides a dynamical analogue of Landauer's principle, and therefore bridges classical communication and thermodynamics. As another implication, we show that, in bipartite settings, classically correlated local baths can admit classical communication even when both local systems are completely thermalized. Hence, thermalizations can transmit information by accessing only classical correlation as a resource. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory., Comment: 6+17 pages; 1+1 figures. New results are added compared with the previous version

In this paper, we consider a simple discrete-time optimal betting problem using the celebrated Kelly criterion, which calls for maximization of the expected logarithmic growth of wealth. While the classical Kelly betting problem can be solved via standard concave programming technique, an alternative but attractive approach is to invoke a Taylor-based approximation, which recasts the problem into quadratic programming and obtain the closed-form approximate solution. The focal point of this paper is to fill some voids in the existing results by providing some interesting properties when such an approximate solution is used. Specifically, the best achievable betting performance, positivity of expected cumulative gain or loss and its associated variance, expected growth property, variance of logarithmic growth, and results related to the so-called survivability (no bankruptcy) are provided., Comment: To appear in the proceedings of the 2020 IEEE Conference on Control Technology and Applications (CCTA)

The takeoff point of this paper is to generalize the existing stock trading results for a class of affine feedback controller to include consideration of a stop-loss order. Using the geometric Brownian motion as the underlying stock price model, our main result is to provide a closed-form expression for the cumulative distribution function for the trading profit or loss. In addition, we show that the affine feedback controller with stop-loss order indeed generalizes the result without stop order in the sense of distribution function. Some simulations and illustrative examples are also provided as supporting evidence of the theory. Moreover, we provide some technical results aimed at addressing the issues about survivability, cash-financing considerations, long-only property, and lower bound of the expected gain or loss., Comment: SIAM Journal on Control and Optimization (SICON)

In this paper, we consider a discrete-time portfolio with $m \geq 2$ assets optimization problem which includes the rebalancing~frequency as an additional parameter in the maximization. The so-called Kelly Criterion is used as the performance metric; i.e., maximizing the expected logarithmic growth of a trader's account, and the portfolio obtained is called the frequency-based Kelly optimal portfolio. The focal point of this paper is to extend upon the results of our previous work to obtain various optimality characterizations on the portfolio. To be more specific, using Kelly's criterion in our frequency-based formulation, we first prove necessary and sufficient conditions for the frequency-based Kelly optimal portfolio. With the aid of these conditions, we then show several new optimality characterizations such as expected ratio optimality and asymptotic relative optimality, and a result which we call the Extended Dominant Asset Theorem. That is, we prove that the $i$th asset is dominant in the portfolio if and only if the Kelly optimal portfolio consists of that asset only. The word "extended" on the theorem comes from the fact that it was only a sufficiency result that was proved in our previous work. Hence, in this paper, we improve it to involve a proof of the necessity part. In addition, the trader's survivability issue (no bankruptcy consideration) is also studied in detail in our frequency-based trading framework. Finally, to bridge the theory and practice, we propose a simple trading algorithm using the notion called dominant asset condition to decide when should one triggers a trade. The corresponding trading performance using historical price data is reported as supporting evidence., Comment: Submitted to IEEE Control Systems Letter

Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability, which is constructed as a channel resource theory induced by a state resource theory. We provide two general classes of resource preservability monotones: One is based on state resource monotones, and another is based on channel distance measures. Specifically, the latter gives the robustness monotone, which has been recently found to have an operational interpretation. As examples, we show that athermality preservability of a Gibbs-preserving channel can be related to the smallest bath size needed to thermalize all its outputs, and it also bounds the capacity of a classical communication scenario under certain thermodynamic constraints. We further apply our theory to the study of entanglement preserving local thermalization (EPLT) and provide a new family of EPLT which admits arbitrarily small nonzero entanglement preservability and free entanglement preservation at the same time. Our results give the first systematic and general formulation of the resource preservation character of free operations., Comment: 14+25 pages, 1 figure, new results added, acknowledgments section updated. Accepted for publication in Quantum. See also related work by Saxena et al. focusing on quantum coherence (arXiv:1910.00708)

Stock trading based on Kelly's celebrated Expected Logarithmic Growth (ELG) criterion, a well-known prescription for optimal resource allocation, has received considerable attention in the literature. Using ELG as the performance metric, we compare the impact of trade execution delay on the relative performance of high-frequency trading versus buy and hold. While it is intuitively obvious and straightforward to prove that in the presence of sufficiently high transaction costs, buy and hold is the better strategy, is it possible that with no transaction costs, buy and hold can still be the better strategy? When there is no delay in trade execution, we prove a theorem saying that the answer is ``no.'' However, when there is delay in trade execution, we present simulation results using a binary lattice stock model to show that the answer can be ``yes.'' This is seen to be true whether self-financing is imposed or not., Comment: Has been accepted to the IEEE Conference on Decision and Control, 2019

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics., Comment: 6+7 pages, 1 figure, closed to the published version

Next-generation xenon detectors with multi-ton-year exposure are powerful direct probes of dark matter candidates, in particular the favorite weakly-interacting massive particles. Coupled with the features of low thresholds and backgrounds, they are also excellent telescopes of solar neutrinos. In this paper, we study the discovery potential of ton-scale xenon detectors in electromagnetic moments of solar neutrinos. Relevant neutrino-atom scattering processes are calculated by applying a state-of-the-arts atomic many-body method--relativistic random phase approximation (RRPA). Limits on these moments are derived from existing data and estimated with future experiment specifications. With one ton-year exposure, XENON-1T can improve the effective milli-charge constraint by a factor two. With LZ and DARWIN, the projected improvement on the solar neutrino effective milli-charge(magnetic moment) is around 7(2) times smaller than the current bound. If LZ can keep the same background level and push the electron recoil threshold to 0.5 keV, the projected improvement on milli-charge(magnetic moment) is about 10(3) times smaller than the current bound.

We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $\alpha$ and a sequence $v(k)$ which models asset returns which are within known bounds but otherwise arbitrary. We introduce two thresholds, $\alpha_-$ and $\alpha_+$, depending on these bounds, and prove that for $\alpha < \alpha_-$, state positivity is guaranteed for all time and all asset-return sequences; i.e., bankruptcy is ruled out and positive solutions of the state equation are continuable indefinitely. On the other hand, for $\alpha > \alpha_+$, we show that there is always a sequence of asset returns for which the state fails to be positive for all time; i.e., along this sequence, bankruptcy is certain and the solution of the state equation ceases to be meaningful after some finite time. Finally, this paper also includes a conjecture which says that for the "gap" interval $\alpha_- \leq \alpha \leq \alpha_+,$ state positivity is also guaranteed for all time. Support for the conjecture, both theoretical and computational, is provided., Comment: Accepted to IEEE Transactions on Automatic Control