Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal order is found to have the capability of accomplishing tasks that are not possible without it. Specifically, we show how this novel class of resource comes into play in quantum batteries by first, combining two static unitary chargers into a coherently superposed one to fully charge an empty battery even if in the presence of battery's local Hamiltonian. Then we demonstrate for a non-unitary charging protocol, the indefinite causal order version charger yields a charged battery with higher energy over its classical counterpart under any conditions. We also have a finding that runs counter to our intuition which, roughly speaking, has the implication that a relatively less powerful charger guarantees a charged battery with higher energy. Finally, to reduce the cost imposed by a measurement-based protection scheme, indefinite causal order shows its potential to fulfill this goal.
Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal order is found to have the capability of accomplishing tasks that are not possible without it. Specifically, we show how this novel class of resource comes into play in quantum batteries by first, combining two static unitary chargers into a coherently superposed one to fully charge an empty battery even if in the presence of battery's local Hamiltonian. Then we demonstrate for a non-unitary charging protocol, the indefinite causal order version charger yields a charged battery with higher energy over its classical counterpart under any conditions. We also have a finding that runs counter to our intuition which, roughly speaking, has the implication that a relatively less powerful charger guarantees a charged battery with higher energy. Finally, to reduce the cost imposed by a measurement-based protection scheme, indefinite causal order shows its potential to fulfill this goal.
In the standard quantum theory, the causal order of occurrence between events is prescribed, and must be definite. This has been maintained in all conventional scenarios of operation for quantum batteries. In this study we take a step further to allow the charging of quantum batteries in an indefinite causal order (ICO). We propose a nonunitary dynamics-based charging protocol and experimentally investigate this using a photonic quantum switch. Our results demonstrate that both the amount of energy charged and the thermal efficiency can be boosted simultaneously. Moreover, we reveal a counterintuitive effect that a relatively less powerful charger guarantees a charged battery with more energy at a higher efficiency. Through investigation of different charger configurations, we find that ICO protocol can outperform the conventional protocols and gives rise to the anomalous inverse interaction effect. Our findings highlight a fundamental difference between the novelties arising from ICO and other coherently controlled processes, providing new insights into ICO and its potential applications.
Enhancement of quantum battery performance is a popular subject in quantum thermodynamics. An interesting phenomenon is the quick charging effect [Phys. Rev. Res. 6, 023136 (2024)], which has been explored by utilizing a quantum interferometric technique known as superposition of trajectories. A similar technique used to boost quantum battery performance is indefinite causal order. Here, we propose a new charging protocol that utilizes cyclic indefinite causal order, whereby N charging sequences are superposed when utilizing N chargers. We observe charging efficiency bursts when implementing our cyclic indefinite charging protocol. The duration of these bursts increase with N. Additionally, we present a circuit model to implement our charging protocol for the two-charger scenario and perform proof-of-concept demonstrations on IonQ, Quantinuum and IBMQ quantum processors. The results validate the existence of charging efficiency bursts as shown by our theoretical analysis and numerical simulations.
In recent years, quantum battery (QB) models have emerged as crucial platforms for exploring the connections between quantum effects and energy within the framework of quantum thermodynamics. Inspired by the physical implementation of quantum switch (QS), we, in this work, present a simple QB model in which a two-level system as battery, under a series of coherent chargers, performs the indefinite causal order (ICO) charging by introducing a control qubit as QS. Within the energy-preserving collision interaction framework, we analyze the charging ICO and conventional definite causal order (DCO) dynamics, respectively, and discover the underlying connection between the final charged states of battery in ICO and DCO charging modes. That is, the ICO charged state can be understood as a split of the DCO charged state, accompanied by an offset caused by the interference component characterizing the ICO effect. That provides direct theoretical evidence that the ICO effect positively influences the ergotropy (i.e., the maximum extractable work) of QB only when quantum coherence is present in the charging process, and it is independent of the average stored energy of the QB. By combining numerical simulations, we examine that quantum coherence in our model is a strong quantum resource contributing to the ergotropy of QB, while the ICO effect plays a catalyst-like role, assisting quantum coherence in further enhancing the ergotropy of the battery. In addition, we also demonstrate that increasing the number of chargers also benefits the optimal ergotropy of QB. Finally, we reveal that, when the coherent chargers are subject to the dephasing channel, the ICO charging mode is more robust against dephasing noise than the DCO charging mode. This investigation deepens our understanding of quantum coherence and the ICO effect in the context of quantum thermodynamics.
Processes with indefinite causal orders (ICOs), such as the quantum switch, are higher-order quantum processes that superpose the order in which quantum operations are performed. Such coherent control yields computational advantages but is not faithfully captured by existing quantum programming languages: either they are restricted to the unitary case, and thus cannot combine ICOs with measurement, or they treat coherent control nonlinearly. In both cases, they do not realize the full computational power of ICOs. We introduce a higher-order quantum functional language that supports general quantum computation, not merely the permutation of channels, and whose linear type system allows quantum control to be well-defined beyond the unitary case, on arbitrary quantum channels. We equip this language with a small-step operational semantics that synchronizes measurement outcomes across superposed branches, using device references and a memory function. We also give a denotational semantics by means of completely positive maps. With linearity as the only constraint, some well-typed terms would denote unphysical maps. We therefore impose a typing discipline that goes beyond linearity, and interpret programs in the causal category Caus[CPM], under which every well-typed program is physically meaningful, a property that can be checked statically and efficiently. We prove soundness, and study the language's expressive power: it can express every quantum channel at first order, and at second order a large subclass of the so-called quantum circuits with quantum control (QC-QCs), containing the quantum switch. Last but not least, we show that this language is well-designed enough to be extended to the nonlinear setting with recursion.
Indefinite causal order is a key feature involved in the study of quantum higher-order transformations. Recently, intense research has been focused on possible advantages related to the lack of definite causal order of quantum processes. Quite often the quantum switch is claimed to provide advantages in information-theoretic and thermodynamic tasks. We address here the question of whether indefinite causal order is a resource for quantum thermodynamics. Inspired by previous results in the literature, we show that indefinite causal order is not necessary for the reported increase in free energy and ergotropy. More specifically, we show that a simple causally ordered process, which replaces the system's state with a new one before the final measurement, outperforms the quantum switch in all thermodynamic tasks considered so far. We further show that a similar advantage can also be achieved without completely discarding system if we allow for non-Markovian interactions between the system and an environment. We extend the analysis to more extreme examples of indefinite causal order, showing that they do not provide an advantage either. Finally, we discuss a possible way to study the advantages that may arise from indefinite causal order in a general scenario.
Hamiltonian k-Locality is the Key Resource for Powerful Quantum Battery Charging
Storing and extracting energy using quantum degrees of freedom is a promising approach to leveraging quantum effects in energy science. Early experimental efforts have already demonstrated its potential to surpass the charging power of existing technologies. In this context, it is crucial to identify the specific quantum effects that can be exploited to design the most efficient quantum batteries and push their performance to the ultimate limit. While entanglement has often been considered a key factor in enhancing charging (or discharging) power, our findings reveal that it is not as critical as previously thought. Instead, three parameters emerge as the most significant in determining the upper bound of instantaneous charging power: the locality of the battery and charger Hamiltonians, and the maximum energy storable in a single unit cell of the battery. To derive this new bound, we have also addressed several open questions previously noted in the literature but lacks an explanation. This bound provides a foundation for designing the most powerful charger-battery systems, where combined optimization of both components offers enhancements that cannot be achieved by manipulating only one of them.