An Energetic Constraint for Qubit-Qubit Entanglement

TL;DR

This paper explores the energetic limits of qubit-qubit entanglement, revealing a trade-off between quantum coherence and entanglement, with implications for optimizing entanglement under energy constraints.

Contribution

It introduces an energetic perspective on entanglement, decomposing energy into coherent and incoherent parts, and relates the coherent energy deficit to entanglement measures.

Findings

Coherent energy is maximal for pure, separable states.

Entanglement reduces the coherent energy, creating a deficit proportional to the square concurrence.

The quantum component of the energy deficit equals the average square concurrence of pure state decompositions.

Abstract

We analyze qubit-qubit entanglement from an energetic perspective and reveal an energetic trade-off between quantum coherence and entanglement. We decompose each qubit internal energy into a coherent and an incoherent component. The qubits' coherent energies are maximal if the qubit-qubit state is pure and separable. They decrease as qubit-qubit entanglement builds up under locally-energy-preserving processes. This yields a ``coherent energy deficit'' that we show is proportional to a well-known measure of entanglement, the square concurrence. In general, a qubit-qubit state can always be represented as a mixture of pure states. Then, the coherent energy deficit splits into a quantum component, corresponding to the average square concurrence of the pure states, and a classical one reflecting the mixedness of the joint state. Minimizing the quantum deficit over the possible pure state decompositions yields the square concurrence of the mixture. Our findings bring out new figures of merit to optimize and secure entanglement generation and distribution under energetic constraints.