Optimal Entangling Capacity of Dynamical Processes

Abstract

We investigate the entangling capacity of dynamical operations when provided with local ancilla. A comparison is made between the entangling capacity with and without the assistance of prior entanglement. An analytic solution is found for the log-negativity entangling capacity of two-qubit gates, which equals the entanglement of the Choi matrix isomorphic to the unitary operator. Surprisingly, the availability of prior entanglement does not affect this result; a property we call resource independence of the entangling capacity. We prove several useful upper-bounds on the entangling capacity that hold for general qudit dynamical operations, and for a whole family of entanglement monotones including log-negativity and log-robustness. The log-robustness entangling capacity is shown to be resource independent for general dynamics. We provide numerical results supporting a conjecture that the log-negativity entangling capacity is resource independence for all two-qudit unitaries.

Changed title since previous version. 8 pages main text + 4 pages of appendices. Rewritten with some mathematical details moved to appendices. Accepted for publication in Physical Review A

References in corpus (20)

• Quantum entanglement
• A computable measure of entanglement
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• The logarithmic negativity: A full entanglement monotone that is not convex
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Robustness of entanglement
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• On the Entangling Power of Quantum Evolutions
• Entanglement of Quantum Evolutions
• Entangling operations and their implementation using a small amount of entanglement
• Quantum dynamics as a physical resource
• Entanglement capabilities of non-local Hamiltonians
• Prospects for measurement-based quantum computing with solid state spins
• Optimal Entanglement Generation from Quantum Operations
• Quantum entanglement of unitary operators on bi-partite systems
• The entangling and disentangling power of unitary transformations are unequal
• Scalable Error Correction in Distributed Ion Trap Computers
• Entangling capacity and distinguishability of two-qubit unitary operators
• An introduction to one-way quantum computing in distributed architectures

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