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

Local Vs. Joint Measurements For The Entanglement Of Assistance

T. Laustsen, Frank Verstraete, S. J. van Enk

Published Jan 1, 2001• 67 citations
OpenAlex

Abstract

We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quart-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?.

Related papers

Local vs. joint measurements for the entanglement of assistance

T. Laustsen, Frank Verstraete, S. J. van Enk

We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quant-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?

Quantum Information and Computation•Jan 1, 2003•53 citations

Local vs. Joint Measurements for the Entanglement of Assistance

T. Laustsen, Frank Verstraete, S. J. van Enk

We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo {\em et al.} ({\tt quant-ph/9803033}) and O. Cohen (Phys. Rev. Lett. {\bf 80}, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?

arXiv:quant-ph/0206192•Jun 27, 2002•7 citations

Entanglement of assistance in three-qubit systems

Klée Pollock, Ge Wang, Eric Chitambar

The entanglement of assistance quantifies the amount of entanglement that can be concentrated among a group of spatially separated parties using the assistance of some auxiliary system. In this paper we study the entanglement of assistance in the simplest scenario of three qubits. We consider how much entanglement is lost when the helper party becomes uncoupled by local measurement and classical communication. For three-qubit pure states, it is found that lossless decoupling is always possible when entanglement is quantified by the maximum probability of locally generating a Bell state. However, with respect to most other entanglement measures, such as concurrence and entanglement entropy, a lossless decoupling of the helper is possible only for a special family of states that we fully characterize.

arXiv:2010.11431•Physical Review A•Mar 22, 2021•7 citations

Joint-measurement advantage and finite-time transitions in accelerated detector registers

Zhiming Huang

The Unruh response thermalizes accelerated detectors, but the entanglement remaining in a register does not by itself specify what distributed measurements can recover. We study this distinction for a four-qubit cluster state whose two assisting nodes independently undergo generalized amplitude damping, while the target nodes remain isolated and the environments are inaccessible. We derive the exact joint-assisted concurrence and the exact one-way value for arbitrary local measurements. The joint optimum equals the bipartition negativity, and computational-basis measurements attain the one-way optimum. A polar-decomposition argument, together with compactness, establishes a necessary and sufficient condition for separable measurements to attain the joint optimum and proves a strict gap whenever this condition fails. For assisting detectors at equal Unruh temperature with relaxation-rate ratio $r>1$, joint advantage exists precisely when the thermal excitation factor satisfies $q<1/r$. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For $r=2$, both the transition time and remaining resource have closed expressions. These results identify when joint assistance is necessary within the independent weak-coupling thermalization model.

quant-pharXiv:2610.19941•Oct 15, 2026•0 citations

Entanglement cost of nonlocal measurements

Somshubhro Bandyopadhyay, Gilles Brassard A, Shelby Kimmel +1 more

For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in $d\ifmmode\times\else\texttimes\fi{}d$ dimensions that is invariant under all local generalized Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.

arXiv:0809.2264•Physical Review A•Jul 15, 2009•44 citations

Coherence of assistance and regularized coherence of assistance

Ming‐Jing Zhao, Teng Ma, Shao-Ming Fei

We study the relation between the coherence of assistance and the regularized coherence of assistance introduced by Chitambar et al. [E. Chitambar et al., Phys. Rev. Lett. 116, 070402 (2016)]. The necessary and sufficient conditions that these two quantities coincide are provided. Detailed examples are analyzed and the optimal pure state decompositions such that the coherence of assistance equals the regularized coherence of assistance are derived. Moreover, we present the protocol for obtaining the maximal relative entropy coherence, assisted by another party under local measurement and one-way communication in one copy setting.

arXiv:1712.09768•Physical Review A•Dec 27, 2017•6 citations
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quart-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?.
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quant-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo {\em et al.} ({\tt quant-ph/9803033}) and O. Cohen (Phys. Rev. Lett. {\bf 80}, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?
The entanglement of assistance quantifies the amount of entanglement that can be concentrated among a group of spatially separated parties using the assistance of some auxiliary system. In this paper we study the entanglement of assistance in the simplest scenario of three qubits. We consider how much entanglement is lost when the helper party becomes uncoupled by local measurement and classical communication. For three-qubit pure states, it is found that lossless decoupling is always possible when entanglement is quantified by the maximum probability of locally generating a Bell state. However, with respect to most other entanglement measures, such as concurrence and entanglement entropy, a lossless decoupling of the helper is possible only for a special family of states that we fully characterize.
The Unruh response thermalizes accelerated detectors, but the entanglement remaining in a register does not by itself specify what distributed measurements can recover. We study this distinction for a four-qubit cluster state whose two assisting nodes independently undergo generalized amplitude damping, while the target nodes remain isolated and the environments are inaccessible. We derive the exact joint-assisted concurrence and the exact one-way value for arbitrary local measurements. The joint optimum equals the bipartition negativity, and computational-basis measurements attain the one-way optimum. A polar-decomposition argument, together with compactness, establishes a necessary and sufficient condition for separable measurements to attain the joint optimum and proves a strict gap whenever this condition fails. For assisting detectors at equal Unruh temperature with relaxation-rate ratio r>1r>1r>1, joint advantage exists precisely when the thermal excitation factor satisfies q<1/rq<1/rq<1/r. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For r=2r=2r=2, both the transition time and remaining resource have closed expressions. These results identify when joint assistance is necessary within the independent weak-coupling thermalization model.
For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in $d\ifmmode\times\else\texttimes\fi{}d$ dimensions that is invariant under all local generalized Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.
We study the relation between the coherence of assistance and the regularized coherence of assistance introduced by Chitambar et al. [E. Chitambar et al., Phys. Rev. Lett. 116, 070402 (2016)]. The necessary and sufficient conditions that these two quantities coincide are provided. Detailed examples are analyzed and the optimal pure state decompositions such that the coherence of assistance equals the regularized coherence of assistance are derived. Moreover, we present the protocol for obtaining the maximal relative entropy coherence, assisted by another party under local measurement and one-way communication in one copy setting.