| ebit | |
|---|---|
| Name | ebit |
| Type | Quantum resource |
| Related | Qubit; Entanglement (quantum); Bell state |
| Introduced | 1990s |
| Unit | ebit |
| Fields | Quantum information theory; Quantum computing |
ebit
An ebit is the standard unit of bipartite pure-state entanglement in Quantum information theory: one maximally entangled two-qubit state (commonly a Bell state) shared between two parties. Eb it quantifies the amount of nonclassical correlation available for quantum tasks and serves as a currency in protocols such as quantum teleportation and superdense coding, making it central to the operational study of entanglement in Quantum Physics.
An ebit is defined operationally as a single copy of a two-qubit maximally entangled state, typically the singlet state |Ψ−⟩ or any of the four Bell states. As a resource it is additive under tensor products: n copies of a Bell pair constitute n ebits. Key properties include invariance under local unitary operations by LOCC that do not change entanglement, monotonicity under LOCC transformations, and the conversion role as a standard unit for asymptotic interconversion of pure-state entanglement via entanglement concentration and entanglement dilution protocols. Eb it is distinct from other measures such as quantum discord and captures the purely nonseparable component of correlations in bipartite pure states.
An ebit is intimately tied to the concept of a Qubit because it is a two-qubit object; one ebit enables the faithful transmission of one qubit of quantum information via quantum teleportation when assisted by classical communication. Quantitatively, for a bipartite pure state |ψ⟩AB, the entanglement in ebits equals the von Neumann entropy S(ρA) = S(ρB) of the reduced state, commonly called the entanglement entropy. Other entanglement measures related to ebits include the Entanglement of formation (expressed in ebits), the Distillable entanglement (number of ebits extractable by LOCC), and the Entanglement cost (ebits required to create the state asymptotically). For mixed states these measures can differ: e.g., a state may have nonzero entanglement of formation but zero distillable entanglement, illustrating irreversibility between ebits consumed and ebits produced.
Ebits function as a currency in many quantum information protocols. In quantum teleportation, one ebit plus two classical bits transmits an arbitrary unknown qubit from sender to receiver. In superdense coding, one ebit allows the transmission of two classical bits using a single qubit channel. Eb it counting also appears in entanglement distillation where noisy shared states are converted into near-perfect Bell pairs using LOCC; the achieved rate defines the distillable entanglement in ebits per input copy. In quantum cryptography, ebits underlie security proofs for protocols like Ekert protocol (E91) where Bell correlations certify secrecy. Resource-theoretic tasks—such as catalytic transformations and reversible interconversion in the asymptotic limit—use ebits as the reference resource to compare different entangled states and to state conversion theorems (e.g., Schumacher–Nielsen coding and the Bennett, Bernstein, Popescu, Schumacher (BBPS) results).
In the resource-theoretic formalism, the set of free operations is typically LOCC and the resource theory quantifies convertibility between states in terms of ebits. The asymptotic equipartition gives that many-copy conversion rates between pure states are governed by the entanglement entropy; hence an arbitrary pure bipartite state with entropy E can be asymptotically converted to E ebits per copy. For mixed states, single-copy and asymptotic conversion rates lead to distinct quantities: Relative entropy of entanglement, entanglement of formation, and distillable entanglement are expressed in ebits or asymptotic ebits per copy. Mathematically, ebits correspond to the rank-one projector onto a Bell state in the Hilbert space H_A ⊗ H_B and are invariant under the action of the group SU(2)⊗SU(2) up to local phases. Resource monotones mapping states to nonincreasing real numbers under LOCC often measure value in ebits.
Experimentally, ebits are realized as entangled photon pairs via spontaneous parametric down-conversion in nonlinear crystals, as entangled electron spins in nitrogen-vacancy centers, in trapped-ion qubits at Max Planck Institute for Quantum Optics and other labs, and in superconducting qubit architectures developed by corporations and institutes such as IBM Quantum and Google AI Quantum. Bell tests performed in experiments (e.g., by groups at Delft University of Technology and University of Vienna) verify generation of high-fidelity ebits and close loopholes in entanglement verification. Practical applications exploiting ebits include quantum key distribution (entanglement-based schemes), distributed quantum computing primitives, quantum repeater links in long-distance quantum communication networks, and benchmarking operations in noisy intermediate-scale quantum (NISQ) devices.
Limitations involving ebits include fragility to decoherence and noise in realistic channels, constraints on distillation rates for mixed states, and the gap between entanglement of formation and distillable entanglement for certain states (bound entanglement). Open problems include characterizing multi-party generalizations of ebits (e.g., GHZ state versus bipartite ebits), computing distillable entanglement for broad classes of mixed states, and optimizing practical distillation and entanglement distribution protocols in presence of realistic noise and finite resources. Further challenges lie in integrating ebits into scalable architectures for fault-tolerant quantum computing and in establishing device-independent certification methods that rely on minimal assumptions about hardware, drawing on results from Bell's theorem and device-independent cryptography. Category:Quantum information theory