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arXiv:2505.05964 · Quantum

Catalytic entanglement transformations with noisy hardware

Hemant Kumar Sharma, Мокеев Александр Сергеевич, Jonas Helsen, Johannes Borregaard

Published May 29, 2026• 0 citations
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Abstract

The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.

DOI
10.22331/q-2026-05-29-2117

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The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.
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.
Auxiliary pure quantum entangled states shared between two parties can act as catalysts in bipartite entanglement transformations. The participation of a catalyst state in the transformation can enhance its success probability. We consider transformations involving entanglement concentration of a finite number of copies of arbitrary two-qubit pure states into a single copy of a maximally entangled two-qubit pure state using bipartite local quantum operations and classical communication aided by a catalyst state. We show the enhancement of success probabilities of the catalyst-assisted procedure compared to the case where no catalysts are used. The optimal two-qubit catalyst and the maximum probability of the transformation using such catalysts can be obtained analytically. The enhancement of concentration success probability using catalysts of higher dimensions is demonstrated numerically. Finally, catalyst aided strategies for obtaining multiple maximally entangled two-qubit states are discussed.
Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of about 1% and incurs polynomial qubit overhead. A recent theorem from the resource theory of coherence shows that catalytic covariant operations amplify coherence at an unbounded rate, but this result has never been cast as an operational protocol. The challenge is to turn an asymptotic theorem into a recovery scheme that works at any noise strength with realistic resources. Here we show that catalytic coherence amplification can be cast as an error-correction primitive, Catalytic Quantum Error Correction (CQEC), which recovers a known target state from noisy copies without any error magnitude threshold whenever the target's coherent modes are preserved. In an effective model of the recovery map, fidelity exceeds 0.99 across 200 noise configurations spanning d = 4-64; the catalyst cost drops from the constructive bound n* ~ d^4 e^(2 gamma) to 32 copies at matched fidelity (10^4- to 10^9-fold) via a pipeline of dynamical decoupling, Clifford twirling, and recursive swap-test purification. A first explicitly CPTP, exactly covariant joint-channel implementation validates genuine recovery under dephasing at small dimension (0.54 -> 0.77) while showing that shallow circuits consume the catalyst, quantifying the model-vs-channel gap. These results turn an abstract resource-theoretic statement into a concrete protocol candidate complementary to stabilizer- and purification-based QEC; an open-source package reproducing the benchmarks accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).
Quantum entanglement is a fundamental resource in quantum information science, commonly consumed to perform tasks like quantum teleportation and quantum key distribution. Entanglement concentration converts partially entangled pure states into nearly perfect Bell pairs. While its efficiency is well understood in the asymptotic limit, practical protocols must operate with finite systems. In this finite regime, and at the low error levels relevant in practice, performance is penalized by corrections that reduce the achievable yield. We investigate whether this fundamental finite-size penalty can be mitigated by an entanglement catalyst: an auxiliary state that aids the transformation but is returned exactly and uncorrupted. Although such a catalyst cannot increase the leading-order asymptotic yield, we show that it fundamentally alters the finite-size scaling. For every bipartite pure state with nonuniform Schmidt coefficients, we exactly determine the optimal second-order correction to the yield and show that catalysis completely overcomes this finite-size penalty.
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.
Quantum catalysts can overcome otherwise impossible quantum state transformations without being consumed, and allowing them to become correlated with the output makes this assistance substantially more powerful. This raises a fundamental question for entanglement theory: which limitations on state manipulation remain when such correlated catalysts are freely available? We answer this question in the positive-partial-transpose (PPT) resource theory, which allows a substantially broader class of operations than local operations and classical communication (LOCC). We identify general conditions under which regularized relative-entropy measures become strongly superadditive, and use them to construct monotones that constrain correlated catalytic PPT transformations without any knowledge of the catalyst. In particular, we prove that the regularized PPT relative entropy is fully additive and strongly superadditive, resolving an open problem in entanglement theory. Most importantly, these constraints show that even arbitrary correlated catalysts cannot restore asymptotic reversibility: for an explicit state, the optimal entanglement distillation rate remains strictly smaller than the entanglement cost. Thus, substantial catalytic assistance does not remove some of the fundamental limitations of mixed-state entanglement manipulation.