Dense Coding Process with Imperfect Encoding Operations

Situ, Haozhen

doi:10.1007/s10773-013-1683-3

Cited by 8 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We highlight some relevant previous work on this problem; this list is not exhaustive. With regard to dense coding: the papers [16,17] dealt with superdense coding over noisy quantum channels or with noisy encoding operations; this can be brought within our framework by considering entanglement-reversibility of N • M w.r.t. a state W , where M is the encoding channel and N is a channel representing the noise.…”

Section: Related Workmentioning

confidence: 99%

“…It follows immediately that dim(A) ≤ dim(B). Now by positivity and faithfulness of the standard trace (17), the isometric 2-morphisms (39) are unitary iff one inequality from (48) and one equality from (49) are equalities (it will then follow that all the inequalities are equalities). We have seen by ( 50) that if dim(A) = dim(B) then the left inequality of (48) is an equality; it may be shown similarly that the left inequality of ( 49) is an equality also, and so the 2-morphisms (39) are unitary.…”

Section: Characterisation In Terms Of Minimal Dilationmentioning

confidence: 99%

See 1 more Smart Citation

Entanglement-invertible channels

Verdon¹

2022

Preprint

View full text Add to dashboard Cite

In a well-known result [26], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to be teleported and the entangled resource must be of dimension d, and the measurement must have d 2 outcomes.In this work we generalise this classification so as to remove the dimensional restriction altogether, thereby resolving an open problem raised in that work. In fact, we classify not just teleportation and dense coding schemes, but entanglement-reversible channels. These are channels between finite-dimensional C * -algebras which are reversible with the aid of an entangled resource state, generalising ordinary reversibility of a channel.In Werner's classification, a bijective correspondence between tight teleportation and dense coding schemes was shown: swapping Alice and Bob's operations turns a teleportation scheme into a dense coding scheme and vice versa. We observe that this property generalises ordinary invertibility of a channel; we call it entanglement-invertibility. We show that entanglement-invertible channels are precisely the quantum bijections previously studied in the setting of quantum combinatorics [11], which are classified in terms of the representation theory of the quantum permutation group.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Characterisation In Terms Of Minimal Dilationmentioning

confidence: 99%

Entanglement-invertible channels

Verdon¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus far, dense coding has been extensively studied in various ways. For example, dense coding that utilises high-dimensional entangled states has been studied in [4,5,6], non-maximally entanglement channels in [7,8,9,10,11,12,13,14,15,16,17,18,19], while multipartite entanglement channels have also been considered in [20,21,22,23,24,25,26,27]. Another generalisation is to perform the communication task under the control of a third party, so-called controlled dense coding [28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Secure N-dimensional simultaneous dense coding and applications

Situ

Qiu

Mateus

et al. 2015

Int. J. Quantum Inform.

View full text Add to dashboard Cite

Simultaneous dense coding guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to "lock" the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on simultaneous dense coding: (1) We propose three simultaneous dense coding protocols, which use different N -dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalise the protocol by implementing the unlocking operation through communication, we improve our protocol's fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of simultaneous dense coding against the intercept-resend attack. (5) We show that simultaneous dense coding can be used to implement a fair contract signing protocol. (6) We also show that the N -dimensional quantum Fourier transform can act as the locking operator in simultaneous teleportation of N -level quantum systems.

show abstract