Von Neumann Entropy from Unitarity

Experimental Catalytic Amplification of Asymmetry

The manipulation and transformation of quantum resources are key parts of quantum mechanics. Among them, asymmetry is one of the most useful operational resources, which is widely used in quantum clocks, quantum metrology, and other tasks. Recent studies have shown that the asymmetry of quantum states can be significantly amplified with the assistance of correlating catalysts that are finite-dimensional auxiliaries. In the experiment, we perform translationally invariant operations, ensuring that the asymmetric resources of the entire system remain nonincreasing, on a composite system composed of a catalytic system and a quantum system. The experimental results demonstrate an asymmetry amplification of 0.0172±0.0022 in the system following the catalytic process. Our Letter showcases the potential of quantum catalytic processes and is expected to inspire further research in the field of quantum resource theories.

Catalytic Advantage in Otto-like Two-Stroke Quantum Engines

We demonstrate how to incorporate a catalyst to enhance the performance of a heat engine. Specifically, we analyze efficiency in one of the simplest engine models, which operates in only two strokes and comprises of a pair of two-level systems, potentially assisted by a d-dimensional catalyst. When no catalysis is present, the efficiency of the machine is given by the Otto efficiency. Introducing the catalyst allows for constructing a protocol which overcomes this bound, while new efficiency can be expressed in a simple form as a generalization of Otto's formula: 1-(1/d)(ω_{c}/ω_{h}). The catalyst also provides a bigger operational range of parameters in which the machine works as an engine. Although an increase in engine efficiency is mostly accompanied by a decrease in work production (approaching zero as the system approaches Carnot efficiency), it can lead to a more favorable trade-off between work and efficiency. The provided example introduces new possibilities for enhancing performance of thermal machines through finite-dimensional ancillary systems.

Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation

Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy conservation. A fundamental question in this setting is how well one can prepare good coherent states from low coherent states and whether a given coherent state is convertible to another one. Here, we show that any low coherent state is convertible to any high coherent state arbitrarily well in two operational settings: asymptotic and catalytic transformations. For a variant of asymptotic coherence manipulation where one aims to prepare desired states in local subsystems, the rate of transformation becomes unbounded regardless of how weak the initial coherence is. In a non-asymptotic transformation with a catalyst, a helper state that locally remains in the original form after the transformation, we show that an arbitrary state can be obtained from any low coherent state. Applying this to the standard asymptotic setting, we find that a catalyst can increase the coherence distillation rate significantly-from zero to infinite rate. We also prove that such anomalous transformation requires small but nonzero coherence in relevant modes, establishing the condition under which a sharp transition of the operational capability occurs. Our results provide a general characterization of the coherence transformability in these operational settings and showcase their peculiar properties compared to other common resource theories such as entanglement and quantum thermodynamics.

Fundamental Limits on Anomalous Energy Flows in Correlated Quantum Systems

In classical thermodynamics energy always flows from the hotter system to the colder one. However, if these systems are initially correlated, the energy flow can reverse, making the cold system colder and the hot system hotter. This intriguing phenomenon is called "anomalous energy flow" and shows the importance of initial correlations in determining physical properties of thermodynamic systems. Here we investigate the fundamental limits of this effect. Specifically, we find the optimal amount of energy that can be transferred between quantum systems under closed and reversible dynamics, which then allows us to characterize the anomalous energy flow. We then explore a more general scenario where the energy flow is mediated by an ancillary quantum system that acts as a catalyst. We show that this approach allows for exploiting previously inaccessible types of correlations, ultimately resulting in an energy transfer that surpasses our fundamental bound. To demonstrate these findings, we use a well-studied quantum optics setup involving two atoms coupled to an optical cavity.

Catalysis of entanglement and other quantum resources

In chemistry, a catalyst is a substance which enables a chemical reaction or increases its rate, while remaining unchanged in the process. Instead of chemical reactions,quantum catalysisenhances our ability to convert quantum states into each other under physical constraints. The nature of the constraints depends on the problem under study and can arise, e.g. from energy preservation. This article reviews the most recent developments in quantum catalysis and gives a historical overview of this research direction. We focus on the catalysis of quantum entanglement and coherence, and also discuss this phenomenon in quantum thermodynamics and general quantum resource theories. We review applications of quantum catalysis and also discuss the recent efforts on universal catalysis, where the quantum state of the catalyst does not depend on the states to be transformed. Catalytic embezzling is also considered, a phenomenon that occurs if the catalyst's state can change in the transition.

Operational Definition of the Temperature of a Quantum State

Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this Letter, we propose such a notion of temperature considering an operational task, inspired by the zeroth law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single- and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis," where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures. We demonstrate our findings using a two-level atom coupled to a single mode of the electromagnetic field.

Catalytic Leverage of Correlations and Mitigation of Dissipation in Information Erasure

Correlations are a valuable resource for quantum information processing and quantum thermodynamics. However, the preparation of some correlated states can carry a substantial cost that should be compared against its value. We show that classical correlations generated in information erasure can be catalytically exploited, which enables us to mitigate the resulting dissipation of heat and entropy. Because these correlations are a byproduct of erasure, they can be considered free. Our framework consists of a composition of two transformations, where an initial erasure transformation is followed by a catalytic mitigation of dissipation. Although we also show that maximum erasure with minimum dissipation and no correlations is theoretically possible, catalysts are always useful in practical erasure settings, where correlations are expected to take place.

A Secured Half-Duplex Bidirectional Quantum Key Distribution Protocol against Collective Attacks

Quantum Key Distribution is a secure method that implements cryptographic protocols. The applications of quantum key distribution technology have an important role: to enhance the security in communication systems. It is originally inspired by the physical concepts associated with quantum mechanics. It aims to enable a secure exchange of cryptographic keys between two parties through an unsecured quantum communication channel. This work proposes a secure half-duplex bidirectional quantum key distribution protocol. The security of the proposed protocol is proved against collective attacks by estimating the interception of any eavesdropper with high probability in both directions under the control of the two parties. A two-qubit state encodes two pieces of information; the first qubit represents the transmitted bit and the second qubit represents the basis used for measurement. The partial diffusion operator is used to encrypt the transmitted qubit state as an extra layer of security. The predefined symmetry transformations induced by unitary in conjunction with the asymmetrical two-qubit teleportation scheme retain the protocol’s secrecy. Compared to the previous protocols, the proposed protocol has better performance on qubit efficiency.

Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence

Quantum resource manipulation may include an ancillary state called a catalyst, which aids the transformation while restoring its original form at the end, and characterizing the enhancement enabled by catalysts is essential to reveal the ultimate manipulability of the precious resource quantity of interest. Here, we show that allowing correlation among multiple catalysts can offer arbitrary power in the manipulation of quantum coherence. We prove that any state transformation can be accomplished with an arbitrarily small error by covariant operations with catalysts that may create a correlation within them while keeping their marginal states intact. This presents a new type of embezzlement-like phenomenon, in which the resource embezzlement is attributed to the correlation generated among multiple catalysts. We extend our analysis to general resource theories and provide conditions for feasible transformations assisted by catalysts that involve correlation, putting a severe restriction on other quantum resources for showing this anomalous enhancement, as well as characterizing achievable transformations in relation to their asymptotic state transformations. Our results provide not only a general overview of the power of correlation in catalysts but also a step toward the complete characterization of the resource transformability in quantum thermodynamics with correlated catalysts.

Entropy and Reversible Catalysis

I show that nondecreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst," whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) catalytic entropy conjecture introduced by Boes et al. [Phys. Rev. Lett. 122, 210402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.210402]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.

Catalytic Transformations of Pure Entangled States

Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We prove that entanglement entropy completely characterizes state transformations in the presence of entangled catalysts. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving asymptotic results an operational meaning also in the single-copy setup.

Novel Technique for Robust Optimal Algorithmic Cooling

Heat-bath algorithmic cooling provides algorithmic ways to improve the purity of quantum states. These techniques are complex iterative processes that change from each iteration to the next and this poses a significant challenge to implementing these algorithms. Here, we introduce a new technique that on a fundamental level, shows that it is possible to do algorithmic cooling and even reach the cooling limit without any knowledge of the state and using only a single fixed operation, and on a practical level, presents a more feasible and robust alternative for implementing heat-bath algorithmic cooling. We also show that our new technique converges to the asymptotic state of heat-bath algorithmic cooling and that the cooling algorithm can be efficiently implemented; however, the saturation could require exponentially many iterations and remains impractical. This brings heat-bath algorithmic cooling to the realm of feasibility and makes it a viable option for realistic application in quantum technologies.