Augmented message-matrix approach to deterministic dense-coding theory

Gerjuoy, E.; Williams, H.T.; Bourdon, Paul S.

doi:10.1103/physreva.79.042315

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…. , L − 1, let S j be the support of ρ j , so that by (8), {S j } L−1 j=0 is a collection of pairwise orthogonal subspaces of H. To send message j to Bob, Alice performs the quantum operation E that creates the state ρ j and sends her qudit to Bob through a noiseless channel, keeping any ancillary particle she may have used in executing E. To decode Alice's message, Bob simply performs a projective measurement described by the observable…”

Section: Decoding Messagesmentioning

confidence: 99%

“…Thus the basis elements are listed in d groups of d elements with the ordering of the groups determined by the second of the pair |ij and the ordering within the groups determined by the first of the pair. This is the ordering used by Gerjuoy et al in [8] to form an augmented message matrix for an original-protocol unitary encoding of messages.…”

Section: E Ancilla Measurementmentioning

confidence: 99%

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Overcoming a limitation of deterministic dense coding with a nonmaximally entangled initial state

Bourdon

Gerjuoy

2010

Phys. Rev. A

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Under two-party deterministic dense coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state | . If | represents a maximally entangled state (i.e., each of its Schmidt coefficients isthen Alice can convey to Bob one of d 2 distinct messages. If | is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d 2 − 1 messages. Encoding d 2 − 2 messages is possible; see, for example, the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when | is not maximally entangled, the communications limit of d 2 − 2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of | is sufficiently close to √ 1/d. In this protocol, d 2 − 2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d 2 − 1)-th message is encoded via a non-trace-preserving quantum operation.PHYSICAL REVIEW A 81, 022314 (2010) no message only when Alice wishes to send the (d 2 − 1)-th message and her encoding procedure fails. We conclude the article with a detailed example illustrating how Alice and Bob can, with probability exceeding 97%, use a two-qubit system in state | = 9 4 √ 10 |00 + √ 79 4 √ 10 |11 as a resource for the communication of three perfectly distinguishable messages (via a two-dimensional noiseless quantum channel). In this example, the probability of success rises to more than 98% if Alice and Bob are willing to tolerate a small chance of Bob's incorrectly interpreting a message.We note that the d = 2 case of the result of Sec. III of this article appears in Appendix A of [6].

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Section: Decoding Messagesmentioning

confidence: 99%

Section: E Ancilla Measurementmentioning

confidence: 99%

Overcoming a limitation of deterministic dense coding with a nonmaximally entangled initial state

Bourdon

Gerjuoy

2010

Phys. Rev. A

Self Cite

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“…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.

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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.

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Dense Coding Process with Imperfect Encoding Operations

Situ

2013

Int J Theor Phys

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Augmented message-matrix approach to deterministic dense-coding theory

Abstract: A method is presented for producing analytical results applicable to the standard two-party deterministic dense coding protocol, wherein communication of K perfectly distinguishable messages is attainable with the aid of K

Cited by 3 publications

References 7 publications

Overcoming a limitation of deterministic dense coding with a nonmaximally entangled initial state

Overcoming a limitation of deterministic dense coding with a nonmaximally entangled initial state

Secure N-dimensional simultaneous dense coding and applications

Dense Coding Process with Imperfect Encoding Operations

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