All teleportation and dense coding schemes

By Reinhard F. Werner. 2000

378 citations recorded by the source corpus.

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert–Schmidt scalar product and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be `tight' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d 2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin squares and complex Hadamard matrices is also presented.

Subfields: Applied Mathematics, Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/843fad1c2f8d846bb030e8e334a3c32501a08cdc

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In Applied Mathematics

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Generating random density matrices (2010, background): “Then the set of N(2) maximally entangled states, |Ψi 〉 = (Ui ⊗ 1)|Ψ+BC〉, forms a maximally entangled basis, which are known to exist in any dimension [35].”
The Theory of Quantum Information (2018, methodology): “Various generalizations of these procedures have been discovered—the general presentation of teleportation and dense coding in this chapter is based on work of Werner [227].”
A Concise Guide to Complex Hadamard Matrices (2005, background): “On the other hand, Hadamard matrices find numerous applications in several problems of theoretical physics.”
Genuinely multipartite entangled states and orthogonal arrays (2014, background): “As it is often the case [54], the theory of quantum information can benefit from combinatorics and Hadamard matrices.”
Construction, classification and parametrization of complex Hadamard matrices (2011, background): “Complex Hadamard matrices of order n are related to Mutually Unbiased Bases (MUBs), a geometric configuration of vectors in C; an object which has wide range of applications in quantum information theory due to a celebrated result of Werner [144].”
Fundamental limits of repeaterless quantum communications (2015, neutral): “he BDSW simulation for channel reproducibility [S57] 2001 Bowen and Bose show that the BDSW simulation can only simulate Pauli channels [S58] 2001 Werner discusses generalized teleportation protocols [S56] 2008 Ji et al. use a deterministic PQGA to simulate certain DV channels in the context of quan”
The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, background): “In particular, is it necessary to have a maximally entangled state? The answer was given by Werner [142], who showed that the family of teleportation schemes described in Example 6.”
Geometry of Quantum States: Index (2007, background): “Two famous examples of this are quantum dense coding [123] and quantum teleportation [117], both of which can be understood [960] using the unitary operator bases introduced in Section 12.”
Defect of a unitary matrix (2007, background): “The search for complex Hadamard matrices [8, 12] is also motivated by the theory of quantum information processing [13, 14, 15].”