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

Zeitschrift für Naturforschung A

Entanglement Capability of Two-qubit Operations

Barbara Kraus, Wolfgang Dür, Guifré Vidal, J. I. Cirac, Maciej Lewenstein, Noah Linden, Sandu Popescu

Published Feb 1, 2001• 9 citations
Publisher

Abstract

Abstract We study the optimal way of creating bi-partite entanglement using a general two-qubit in­ teraction. On the one hand, we analyze the entanglement capability of an arbitrary non-local Hamiltonian acting on two qubits. We explicitly calculate the state which maximizes the entangle­ ment produced per time step 81 during the non-local evolution. On the other hand, we determine the maximal amount of entanglement which can be produced by an arbitrary two-qubit gate. We also give the separable state which leads to the output state containing this amount of entanglement. Furthermore, we consider the situation where auxiliary systems are present. Finally, we determine the non-unitary processes which are able to create entanglement from an initially separable state of two systems.

DOI
10.1515/zna-2001-0114

Related papers

Entanglement Capabilities of Nonlocal Hamiltonians

Wolfgang Dür, Guifré Vidal, J. I. Cirac +2 more

We quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We give a procedure for optimizing the generation of entanglement. We also show that a Hamiltonian can create more entanglement if one uses auxiliary systems.

arXiv:quant-ph/0006034•Physical Review Letters•Sep 10, 2001•172 citations

Optimal entanglement generation in GHZ-type states

Natalia Giovenale, L Hernandez-Martinez, A. P. Majtey +1 more

Abstract The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.

Journal of Physics A Mathematical and Theoretical•Nov 7, 2023•1 citation

Optimal simulation of two-qubit Hamiltonians using general local operations

C. H. Bennett, J. I. Cirac, Matthew Leifer +4 more

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian $H\ensuremath{\ne}{H}_{A}{+H}_{B}.$ We consider the achievable space of Hamiltonians ${H}^{\ensuremath{'}}$ such that the evolution ${e}^{\ensuremath{-}{\mathrm{iH}}^{\ensuremath{'}}t}$ can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and ${H}^{\ensuremath{'}},$ there exists a scale factor s such that for all times t the evolution ${e}^{\ensuremath{-}{\mathrm{iH}}^{\ensuremath{'}}\mathrm{st}}$ can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and ${H}^{\ensuremath{'}},$ we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.

arXiv:quant-ph/0107035•Physical Review A•Jul 19, 2002•110 citations

Optimal entanglement generation in GHZ-type states

Natalia Giovenale, Hernandez-Martinez, L., A. P. Majtey +1 more

The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored.Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyse the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.

arXiv:2310.17365•Oct 26, 2023•0 citations

Optimizing for an arbitrary perfect entangler. I. Functionals

Paul Watts, Jiří Vala, Matthias M. Müller +5 more

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.

arXiv:1412.7347•Physical Review A•Jun 8, 2015•60 citations

Optimal simulations of two-qubit Hamiltonians using general local operations

CH Bennett, JI Cirac, MS Leifer +4 more

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian Hnot equalH(A)+H-B. We consider the achievable space of Hamiltonians H-' such that the evolution e(-iH')t can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H-', there exists a scale factor s such that for all times t the evolution e(-iH')st can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H-', we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.

•Jul 1, 2002•0 citations
Abstract We study the optimal way of creating bi-partite entanglement using a general two-qubit in­ teraction. On the one hand, we analyze the entanglement capability of an arbitrary non-local Hamiltonian acting on two qubits. We explicitly calculate the state which maximizes the entangle­ ment produced per time step 81 during the non-local evolution. On the other hand, we determine the maximal amount of entanglement which can be produced by an arbitrary two-qubit gate. We also give the separable state which leads to the output state containing this amount of entanglement. Furthermore, we consider the situation where auxiliary systems are present. Finally, we determine the non-unitary processes which are able to create entanglement from an initially separable state of two systems.
Abstract The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian $H\ensuremath{\ne}{H}_{A}{+H}_{B}.$ We consider the achievable space of Hamiltonians ${H}^{\ensuremath{'}}$ such that the evolution ${e}^{\ensuremath{-}{\mathrm{iH}}^{\ensuremath{'}}t}$ can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and ${H}^{\ensuremath{'}},$ there exists a scale factor s such that for all times t the evolution ${e}^{\ensuremath{-}{\mathrm{iH}}^{\ensuremath{'}}\mathrm{st}}$ can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and ${H}^{\ensuremath{'}},$ we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.
The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored.Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyse the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian Hnot equalH(A)+H-B. We consider the achievable space of Hamiltonians H-' such that the evolution e(-iH')t can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H-', there exists a scale factor s such that for all times t the evolution e(-iH')st can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H-', we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.