Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0403170 · Physical Review A

When catalysis is useful for probabilistic entanglement transformation

Yuan Feng, Runyao Duan, Mingsheng Ying

Published Jun 9, 2004• 12 citations
arXivHTMLPDF

Abstract

We determine all $2\ifmmode\times\else\texttimes\fi{}2$ quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a sufficient and necessary condition is derived under which a certain probabilistic transformation has useful catalysts.

DOI
10.1103/physreva.69.062310

Related papers

Catalyst-Assisted Probabilistic Entanglement Transformation

Y. Feng, Runyao Duan, Mingsheng Ying

We are concerned with catalyst-assisted probabilistic entanglement transformations. A necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement transformation. We also design an algorithm which leads to an efficient method for finding the most economical partial catalysts with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully investigated.

arXiv:quant-ph/0404154•IEEE Transactions on Information Theory•Feb 28, 2005•21 citations

1 Catalyst-assisted Probabilistic Entanglement Transformation

Yuan Feng, Runyao Duan, Mingsheng Ying

Abstract — We examine catalyst-assisted probabilistic entanglement transformations. A sufficient and necessary condition of when some appropriate catalyst exists that can increase the maximal transformation probability is presented. We also design an algorithm which leads to an efficient method to find the most economical partial catalyst with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully examined. Index Terms — Probabilistic entanglement transformation, catalyst-assisted transformation, partial catalyst.

•Jan 1, 2004•14 citations

An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation

Runyao Duan, Yuan Feng, Mingsheng Ying

We examine the powers of entanglement-assisted transformation and multiple-copy entanglement transformation. First, we find a sufficient condition of when a given catalyst is useful in producing another specific target state. As an application of this condition, for any non-maximally entangled bipartite pure state and any integer $n$ not less than 4, we are able to explicitly construct a set of $n\times n$ quantum states which can be produced by using the given state as a catalyst. Second, we prove that for any positive integer $k$, entanglement-assisted transformation with $k\times k$-dimensional catalysts is useful in producing a target state if and only if multiple-copy entanglement transformation with $k$ copies of state is useful in producing the same target. Moreover, a necessary and sufficient condition for both of them is obtained in terms of the Schmidt coefficients of the target. This equivalence of entanglement-assisted transformation and multiple-copy entanglement transformation implies many interesting properties of entanglement transformation. Furthermore, these results are generalized to the case of probabilistic entanglement transformations.

arXiv:quant-ph/0404046•Apr 7, 2004•3 citations

Advantage of flexible catalysis for entanglement and quantum thermodynamics

Jingsong Ao, Aby Philip, Alexander Streltsov

Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.

quant-pharXiv:2603.05146•Physical Review A•Mar 6, 2026•0 citations

Trade-off between multiple-copy transformation and entanglement catalysis

Runyao Duan, Yuan Feng, Xin Li +1 more

We demonstrate that multiple copies of a bipartite entangled pure state may serve as a catalyst for certain entanglement transformations while a single copy cannot. Such a state is termed a ``multiple-copy catalyst'' for the transformations. A trade-off between the number of copies of source state and that of the catalyst is also observed. These results can be generalized to probabilistic entanglement transformations directly.

arXiv:quant-ph/0312010•Physical Review A•Jun 8, 2005•12 citations

Catalytic transformations for bipartite pure states

S. Turgut

Entanglement catalysis is a phenomenon that usually enhances the conversion probability in the transformation of entangled states by the temporary involvement of another entangled state (so-called catalyst), where after the process is completed the catalyst is returned to the same state. For some pairs of bipartite pure entangled states, catalysis enables a transformation with unit probability of success, in which case the respective Schmidt coefficients of the states are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation. This paper provides all necessary and sufficient conditions for the trumping and two other associated relations. Using these conditions, the least upper bound of conversion probabilities using catalysis is also obtained. Moreover, best conversion ratios achievable with catalysis are found for transformations involving many copies of states.

arXiv:0706.3654•Journal of Physics A Mathematical and Theoretical•Sep 18, 2007•96 citations
We determine all 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a sufficient and necessary condition is derived under which a certain probabilistic transformation has useful catalysts.
We are concerned with catalyst-assisted probabilistic entanglement transformations. A necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement transformation. We also design an algorithm which leads to an efficient method for finding the most economical partial catalysts with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully investigated.
Abstract — We examine catalyst-assisted probabilistic entanglement transformations. A sufficient and necessary condition of when some appropriate catalyst exists that can increase the maximal transformation probability is presented. We also design an algorithm which leads to an efficient method to find the most economical partial catalyst with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully examined. Index Terms — Probabilistic entanglement transformation, catalyst-assisted transformation, partial catalyst.
We examine the powers of entanglement-assisted transformation and multiple-copy entanglement transformation. First, we find a sufficient condition of when a given catalyst is useful in producing another specific target state. As an application of this condition, for any non-maximally entangled bipartite pure state and any integer nnn not less than 4, we are able to explicitly construct a set of n×nn\times nn×n quantum states which can be produced by using the given state as a catalyst. Second, we prove that for any positive integer kkk, entanglement-assisted transformation with k×kk\times kk×k-dimensional catalysts is useful in producing a target state if and only if multiple-copy entanglement transformation with kkk copies of state is useful in producing the same target. Moreover, a necessary and sufficient condition for both of them is obtained in terms of the Schmidt coefficients of the target. This equivalence of entanglement-assisted transformation and multiple-copy entanglement transformation implies many interesting properties of entanglement transformation. Furthermore, these results are generalized to the case of probabilistic entanglement transformations.
Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.
Entanglement catalysis is a phenomenon that usually enhances the conversion probability in the transformation of entangled states by the temporary involvement of another entangled state (so-called catalyst), where after the process is completed the catalyst is returned to the same state. For some pairs of bipartite pure entangled states, catalysis enables a transformation with unit probability of success, in which case the respective Schmidt coefficients of the states are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation. This paper provides all necessary and sufficient conditions for the trumping and two other associated relations. Using these conditions, the least upper bound of conversion probabilities using catalysis is also obtained. Moreover, best conversion ratios achievable with catalysis are found for transformations involving many copies of states.