Abstract: So-called Thermal Operations seem to describe the most fundamental, and reasonable, set of operations allowable for state transformations at an ambient inverse temperature β. However, a priori, they require experimentalists to manipulate very complex environments and have control over their internal degrees of freedom. For this reason, the community has been working on creating more experimentally-friendly operations. In [Perry et al., Phys. Rev. X 8, 041049] it was shown that for states diagonal in the energy basis, that Thermal Operations can be performed by so-called Coarse Operations, which need just one auxiliary qubit, but are otherwise Markovian and classical in spirit. In this work, by providing an explicit counterexample, we show that this one qubit of memory is necessary. We also fully characterize the possible transitions that do not require memory for the system being a qubit. We do this by analyzing arbitrary control sequences comprising level energy changes and partial thermalizations in each step.

Links: arXiv:2009.03110 

Abstract: (...) In this paper, we define a task as a partially ordered set of safety, target, and comfort requirements and introduce an automated methodology to enforce a natural order among requirements into the reward signal. We perform this by automatically translating the requirements into a sum of safety, target, and comfort rewards, where the target reward is a function of the safety reward and the comfort reward is a function of the safety and target rewards. Using a potential-based formulation, we enhance sparse to dense rewards and formally prove this to maintain policy optimality. We call our novel approach hierarchical, potential-based reward shaping (HPRS). Our experiments on eight robotics benchmarks demonstrate that HPRS is able to generate policies satisfying complex hierarchical requirements. Moreover, compared with the state of the art, HPRS achieves faster convergence and superior performance with respect to the rank-preserving policy-assessment metric. By automatically balancing competing requirements, HPRS produces task-satisfying policies with improved comfort and without manual parameter tuning.  (...)

Links: arXiv:2110.02792 Frontiers in Robotics and AI 2024.1444188 

Abstract: We present a method for mining parameters of temporal specifications for signal classification. Given a parametric formula and a set of labeled traces, we find one parameter valuation for each class and use it to instantiate the specification template. The resulting formula characterizes the signals in a class by discriminating them from signals of other classes. We propose a two-step approach: first, for each class, we approximate its validity domain, which is the region of the valuations that render the formula satisfied. Second, we select from each validity domain the valuation that maximizes the distance from the validity domain of other classes. We provide a statistical guarantee that the selected parameter valuation is at a bounded distance from being optimal. Finally, we validate our approach on three case studies from different application domains.

Links: Runtime Verification (2023) 

Abstract: To test automated driving systems, we present a case study for finding critical scenarios in driving environments guided by formal specifications. To that aim, we devise a framework for critical scenario identification, which we base on open-source libraries that combine scenario specification, testing, formal methods, and optimization.

Links: arXiv:2303.05139 Formal Methods (2023) 

Abstract: Reinforcement learning (RL) is a popular approach for robotic path planning in uncertain environments. However, the control policies trained for an RL agent crucially depend on user-defined, state-based reward functions. Poorly designed rewards can lead to policies that do get maximal rewards but fail to satisfy desired task objectives or are unsafe. There are several examples of the use of formal languages such as temporal logics and automata to specify high-level task specifications for robots (in lieu of Markovian rewards). Recent efforts have focused on inferring state-based rewards from formal specifications; here, the goal is to provide (probabilistic) guarantees that the policy learned using RL (with the inferred rewards) satisfies the high-level formal specification. A key drawback of several of these techniques is that the rewards that they infer are sparse: the agent receives positive rewards only upon completion of the task and no rewards otherwise. This naturally leads to poor convergence properties and high variance during RL. In this work, we propose using formal specifications in the form of symbolic automata: these serve as a generalization of both bounded-time temporal logic-based specifications as well as automata. Furthermore, our use of symbolic automata allows us to define non-sparse potential-based rewards which empirically shape the reward surface, leading to better convergence during RL. We also show that our potential-based rewarding strategy still allows us to obtain the policy that maximizes the satisfaction of the given specification. 

Links: arXiv:2202.02404 (2023) Conference on Decision and Control 

Abstract: Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this Letter, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms, or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary high-dimensional mixed states, we implement some three-setting protocols generated by our method. These protocols allow us to experimentally certify two- and three-unfaithful entanglement in four-dimensional photonic states, some of which contain well above 50% of noise. 

Links: arXiv:2011.02217 PhysRevLett.127.220501

Abstract: A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the average game scores achievable by players subject to constraints on their preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general sub-optimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.

Links: arXiv:2011.02216 Nat. Commun. 12, 4553 (2021)   Code 

Abstract: Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Device-independent quantum random number generators (QRNGs) provide a means of completely trusted randomness, but are highly impractical due to their strict technological requirements, such as loophole-free quantum nonlocality. By making fixed assumptions on specific parts of the device, semi-device-independent QRNGs lower these requirements drastically. However, this has usually been done at the cost of limiting their flexibility and security to a specific physical implementation and level of trust. Here we propose and experimentally test a new framework for semi-device-independent randomness certification that employs a flexible set of assumptions, allowing it to be applied in a range of physical scenarios involving both quantum and classical entropy sources. At the heart of our method lies a source of trusted vacuum in the form of a signal shutter, which enables the honesty of partially trusted measurement devices to be tested and provides lower bounds on the guessing probability of their measurement outcomes. We experimentally verify our protocol with a photonic setup and generate secure random bits under three different source assumptions with varying degrees of security and resulting data rates. Our work demonstrates a simple and practical way for achieving semi-device-independent randomness generation with user-defined flexibility in terms of levels of trust and physical implementations. 

Links: arXiv:2002.12295  npj Quantum Information 7,50

Abstract: One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a D-unfaithful state, one that cannot be certified as D-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most D. 

Links: arXiv:1912.10056  PhysRevLett.124.200502 (Press Release)  Code 

Abstract: We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using non-coupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable. 

Links: arXiv:1710.04601  PhysRevLett.120.230503 

Abstract: We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques.

Links: arXiv:1709.04898  PhysRevLett.121.050501 

Abstract: Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of the latter is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in open quantum systems. We show the generic appearance of objective results in quantum measurements, provided we macroscopically coarse-grain the measuring apparatus and wait long enough. To study genericity, we employ the widely-used Gaussian Unitary Ensemble of random matrices and the Hoeffding inequality. We derive generic objectivization timescales, given solely by the interaction strength and the systems' dimensions. Our results are manifestly universal and are a generic property of von Neumann measurements.

Links: arXiv:1604.02011  PhysRevA.96.032124 

Abstract: Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary assumptions that the parties have to make about their devices, giving rise to device-independent QKD (DIQKD). However, in all existing protocols to date the parties need to have an initial (at least partially) random seed as a resource. In this work, we show that this requirement can be dropped. Using recent advances in the fields of randomness amplification and randomness expansion, we demonstrate that it is sufficient for the message the parties want to communicate to be (partially) unknown to the adversaries -- an assumption without which any type of cryptography would be pointless to begin with. One party can use her secret message to locally generate a secret sequence of bits, which can then be openly used by herself and the other party in a DIQKD protocol. Hence, our work reduces the requirements needed to perform secure DIQKD and establish safe communication.

Links: arXiv:1507.05752  PhysRevA.94.022305 

No, your corpuses are Not entangled!

Understanding Bell’s Theorem is hard, but not as hard as breaking physics.

Link: Medium 

Self-Destructive RL Agents

Innocent changes to RL reward functions produce surprising behaviors

Link: Medium