Quantum entanglement as a quantifiable resource
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Quantum mechanical objects can exhibit correlations with one another that are fundamentally at odds with the paradigm of classical physics; one says that the objects are 'entangled'. In the past few years, entanglement has come to be studied not only as a marvel of nature but as a potential resource, particularly as a resource for certain unusual kinds of communication. This paper reviews two such uses of entanglement, called 'teleportation' and 'dense coding'. Teleportation is the direct,
... is the direct, though not instantaneous, transfer of a quantum state from one object to another over a distance. Dense coding is the effective doubling of the information-carrying capacity of a quantum particle through prior entanglement with a particle at the receiving end. The final section of the paper presents various quantitative measures of entanglement and considers novel features that arise when entanglement is shared among three objects. where a, b, c and d are complex numbers such that |a| 2 + |b| 2 + |c| 2 + |d| 2 = 1, and |↑↑ , for example, is the state in which both spins are pointing up. Some states of the form (1.1) can be factorized into separate states of the individual particles via the tensor product ⊗ (e.g. |↑ ⊗ |↓ = |↑↓ ). It happens that such factorization can be done only if ad − bc = 0, so that most states of the form (1.1) do not factorize. The non-factorizable states are called entangled and are characterized by † There do exist more general 'non-orthogonal' measurements (Helstrom 1976; Peres 1990), but they still do not allow a perfect discrimination between directions that are not diametrically opposed. ‡ As with measurements, quantum mechanics allows more general transformations, usually involving a quantum interaction with another object (Kraus 1983), but we will not need such generalized transformations in this paper.