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Entanglement is a quantifiable resource in quantum information theory, analogous to fuel or currency that is consumed to perform tasks impossible with classical communication alone. The resource-theoretic framework defines free operations (local operations and classical communication, LOCC) and identifies entanglement as the resource that LOCC alone cannot create. Entanglement enables quantum teleportation, superdense coding, and enhanced communication capacity. Measures like entanglement entropy, concurrence, and entanglement of formation quantify how much entanglement a state contains. Bell pairs are the standard unit: one ebit (entanglement bit) denotes the entanglement in a maximally entangled two-qubit state.
In classical information theory, the fundamental resource is communication bandwidth — bits per second through a channel. In quantum information theory, there are three distinct resources: quantum communication (qubits), classical communication (bits), and entanglement (ebits, shared entangled pairs). The resource theory of entanglement formalizes the role of entanglement as a consumable resource that enhances the power of classical and quantum communication.
The framework is built on the concept of LOCC — local operations and classical communication. Alice and Bob can each perform arbitrary quantum operations on their local systems and communicate classically, but they cannot send quantum systems to each other (unless they consume pre-shared entanglement via teleportation). Under LOCC, entanglement cannot be created from scratch — two initially unentangled parties remain unentangled no matter how much classical communication they exchange. This makes entanglement a genuine resource: it enables capabilities beyond what LOCC alone provides.
The canonical demonstrations are teleportation and superdense coding, which you have already studied. Teleportation converts 1 ebit + 2 classical bits into 1 qubit of quantum communication. Superdense coding converts 1 ebit + 1 qubit into 2 classical bits of communication. These are exact, one-shot conversions. In both cases, the shared Bell pair is consumed: after the protocol, Alice and Bob are no longer entangled. The entanglement was the fuel that powered the enhanced communication, and like fuel, it is spent in the process.
Entanglement measures quantify the resource. The entanglement entropy of a pure bipartite state |psi_AB> is the von Neumann entropy of either reduced state: S(rho_A) = -Tr(rho_A log rho_A). For a Bell state, this equals 1 ebit. For a product state, it equals 0. The entanglement of formation E_f generalizes this to mixed states — the minimum average entanglement entropy over all pure-state decompositions. The distillable entanglement E_d is the rate at which Bell pairs can be extracted from many copies using LOCC. A remarkable phenomenon is bound entanglement: some mixed states have E_f > 0 (they cost entanglement to prepare) but E_d = 0 (no Bell pairs can be distilled from them). This irreversibility — entanglement that can be created but not recovered — has no classical analog and remains one of the deepest puzzles in quantum information theory.
The resource theory extends to multipartite entanglement and quantum networks, where different types of entanglement (GHZ states, W states, cluster states) serve as resources for different tasks. The framework provides the foundation for quantum network theory, where entanglement must be distributed, stored, and consumed to enable distributed quantum computation and long-distance quantum communication.