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

Physical Review A

Optimal enhancement of the fidelity of two qubits.

Frank Verstraete, Henri Verschelde

Published Jan 1, 2002• 6 citations
OpenAlex

Abstract

We consider a single copy of a mixed state of two qubits and prove tight lower and upper bounds for its fidelity in terms of its concurrence or negativity. Next we derive the optimal filtering operations and the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of a given copy of a mixed state of two qubits. The optimal LOCC operations turn out to be very simple and implementable by 1-LOCC protocols, and always yield a fidelity larger then 1/2 if the original state was entangled.

Related papers

Optimal Teleportation with a Mixed State of Two Qubits

Frank Verstraete, Henri Verschelde

We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.

arXiv:quant-ph/0303007•Physical Review Letters•Mar 5, 2003•154 citations

Fidelity of mixed states of two qubits

Frank Verstraete, Henri Verschelde

We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of a convex set of states with constant fidelity, and use this to prove tight lower and upper bounds on the fidelity for a given amount of entanglement.

arXiv:quant-ph/0203073•Physical Review A•Aug 12, 2002•104 citations

Purification of two-qubit mixed states

E. Jan\'e

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

Quantum Information and Computation•Aug 1, 2002•7 citations

Purification of two-qubit mixed states

E. Jané

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

arXiv:quant-ph/0205107•Quantum Information and Computation•May 17, 2002•7 citations

Optimal local preparation of an arbitrary mixed state of two qubits: Closed expression for the single-copy case

Guifré Vidal

We consider the problem of preparing a single copy of an arbitrary two-qubit mixed state $\ensuremath{\rho},$ starting from an entangled pure state $\ensuremath{\psi}$ and using only local operations assisted with classical communication. We present an analytical expression for the minimal amount of pure-state entanglement required, and describe the corresponding local strategy. We also examine optimal probabilistic generalizations of the previous process.

arXiv:quant-ph/0003002•Physical Review A•Nov 14, 2000•26 citations

Optimal estimation of an unknown maximally entangled state with local operations and classical communication

ShengLi Zhang, Xu‐Bo Zou, Ke Li +2 more

We consider the optimal measurement procedures for estimating an unknown maximally entangled state with local operations and classical communications (LOCC). By the ``optimal,'' we mean that there is no other LOCC measurements that can provide a higher estimation fidelity. In fact, we first use the positive partial transpose constraint to obtain an upper bound of the fidelity; then, we show there exists a kind of LOCC measurement that can attain such a bound. The estimation fidelity of the optimal LOCC estimation procedures is $\frac{D+2}{(D+1){D}^{2}}$ with $D$ denoting the dimension of the relevant quantum system.

Physical Review A•Oct 18, 2007•3 citations
We consider a single copy of a mixed state of two qubits and prove tight lower and upper bounds for its fidelity in terms of its concurrence or negativity. Next we derive the optimal filtering operations and the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of a given copy of a mixed state of two qubits. The optimal LOCC operations turn out to be very simple and implementable by 1-LOCC protocols, and always yield a fidelity larger then 1/2 if the original state was entangled.
We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.
We consider the optimal measurement procedures for estimating an unknown maximally entangled state with local operations and classical communications (LOCC). By the ``optimal,'' we mean that there is no other LOCC measurements that can provide a higher estimation fidelity. In fact, we first use the positive partial transpose constraint to obtain an upper bound of the fidelity; then, we show there exists a kind of LOCC measurement that can attain such a bound. The estimation fidelity of the optimal LOCC estimation procedures is D+2(D+1)D2\frac{D+2}{(D+1){D}^{2}}(D+1)D2D+2​ with DDD denoting the dimension of the relevant quantum system.