Entanglement sharing via qudit channels: Nonmaximally entangled states may be necessary for one-shot optimal singlet fraction and negativity

Abstract

We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving LOCC under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension $d\ge 3$, one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. We further show that the generalization of the formula that exactly computes one-shot optimal singlet fraction for qubit channels does not hold in general in higher dimensions. A consequence of our results is that the ordering of entangled states in all finite dimensions may not be preserved under trace-preserving LOCC.

7 pages; v2: minor changes, published version

References in corpus (2)

• Optimal fidelity for a quantum channel may be attained by non-maximally entangled states
• Excessive distribution of quantum entanglement

Cited by in corpus (5)

• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• Repeater-Based Quantum Communication Protocol: Maximizing Teleportation Fidelity with Minimal Entanglement
• Optimal one-shot entanglement sharing
• Distilled remote entanglement between superconducting qubits across optical channels
• Maximum expectation of observables with restricted purity states