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.
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.
We investigate the fundamental constraint on amplifying the asymmetry in quantum states with correlating catalysts. Here a correlating catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated with the quantum system. Interestingly, we prove that under translationally invariant operations, uncorrelating catalysts in pure states are useless in any state transformation, while with a correlating catalyst, one can extend the set of accessible states from an initially asymmetric state. Moreover, we show that the power of a catalyst increases with its dimension, and further, with a large enough catalyst, a qubit state with an arbitrarily small amount of asymmetry can be converted to any mixed qubit state. In doing so, we build a bridge between two important results concerning the restrictions on coherence conversion, the no-broadcasting theorem and the catalytic coherence. Our results may also apply to the constraints on coherence evolution in quantum thermodynamics and to the distribution of timing information between quantum clocks.
Quantum catalysis, the ability to enable previously impossible transformations by using auxiliary systems without degrading them, has emerged as a powerful tool in various resource theories. Although catalytically enabled state transformations have been formally characterized by the monotonic behavior of entropic quantifiers (e.g., the von Neumann entropy or nonequilibrium free energy), such characterizations often rely on unphysical assumptions, namely, the ability of using catalysts of infinitely large dimension. This approach offers very limited insights into the practical significance of using catalysis for quantum information processing. Here, we address this problem across a broad class of quantum resource theories. Leveraging quantum information tools beyond the asymptotic regime, we establish sufficient conditions for the existence of catalytic transformations with finite-size catalysts. We further unveil connections between finite-size catalysis and multicopy transformations. Notably, we discover a phenomenon of catalytic resonance: by carefully tailoring the catalysts's state, one can drastically reduce the required dimension of the catalyst, thus enabling efficient catalytic transformations with minimal resources. Finally, we illustrate our findings with examples from the resource theories of entanglement and thermodynamics, as well in the context of catalytic unitary transformations.
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.
Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.
In the classical regime, thermodynamic state transformations are governed by the free energy. This is also called as the second law of thermodynamics. Previous works showed that, access to a catalytic system allows us to restore the second law in the quantum regime when we ignore coherence. However, in the quantum regime, coherence and free energy are two independent resources. Therefore, coherence places additional nontrivial restrictions on the state transformations that remain elusive. In order to close this gap, we isolate and study the nature of coherence, i.e., we assume access to a source of free energy. We show that allowing catalysis along with a source of free energy allows us to amplify any quantum coherence present in the quantum state arbitrarily. Additionally, any correlations between the system and the catalyst can be suppressed arbitrarily. Therefore, our results provide a key step in formulating a fully general law of quantum thermodynamics.
Entanglement is a key quantum resource in various quantum protocols, with a rich set of laws governing its manipulation. In this context, catalysis refers to the possibility of an auxiliary state that enables a previously forbidden manipulation, while being completely returned at the end. While the catalytic setting has been thoroughly examined in the single-copy regime, much less is known in the asymptotically many copy regime. In this work, we focus on the entanglement cost of preparing asymptotically many copies of a given state exactly. We show that catalysis can significantly lower the exact entanglement cost by constructing an explicit catalytic protocol. Additionally, these findings generalize readily to other resource theories, showing a general catalytic advantage in the resource dilution task.