Add: pages, pmid, authors 1-1. Removed URL that duplicated identifier. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by CorrectionsJackal | Category:Quantum information science | #UCB_Category 121/177
The transmission of two bits via a single qubit is made possible by the fact that Alice can choose among ''four'' [[quantum gate]] operations to perform on her share of the entangled state. Alice determines which operation to perform accordingly to the pair of bits she wants to transmit. She then sends Bob the qubit state ''evolved through the chosen gate''. Said qubit thus encodes information about the two bits Alice used to select the operation, and this information can be retrieved by Bob thanks to pre-shared entanglement between them. After receiving Alice's qubit, operating on the pair and measuring both, Bob obtains two classical bits of information. It is worth stressing that if Alice and Bob do not pre-share entanglement, then the superdense protocol is impossible, as this would violate [[Holevo's theorem]].
Superdense coding is the underlying principle of secure quantum secret coding. The necessity of having both qubits to decode the information being sent eliminates the risk of eavesdroppers intercepting messages.<ref name="Wang2005">{{Cite journal |lastlast1=Wang |firstfirst1=Chuan |last2=Deng |first2=Fu-Guo |last3=Li |first3=Yan-Song |last4=Liu |first4=Xiao-Shu |last5=Long |first5=Gui Lu |date=2005-04-28 |title=Quantum secure direct communication with high-dimension quantum superdense coding |url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.044305 |journal=Physical Review A |volume=71 |issue=4 |pages=044305 |doi=10.1103/PhysRevA.71.044305}}</ref>
== Overview ==
Line 132:
== Experimental ==
The protocol of superdense coding has been actualized in several experiments using different systems to varying levels of channel capacity and fidelities. In 2004, trapped [[beryllium-9]] ions were used in a maximally entangled state to achieve a channel capacity of 1.16 with a fidelity of 0.85.<ref name="Schaetz2004">{{Cite journal |lastlast1=Schaetz |firstfirst1=T. |last2=Barrett |first2=M. D. |last3=Leibfried |first3=D. |last4=Chiaverini |first4=J. |last5=Britton |first5=J. |last6=Itano |first6=W. M. |last7=Jost |first7=J. D. |last8=Langer |first8=C. |last9=Wineland |first9=D. J. |date=2004-07-22 |title=Quantum Dense Coding with Atomic Qubits |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.93.040505 |journal=Physical Review Letters |volume=93 |issue=4 |pages=040505 |doi=10.1103/PhysRevLett.93.040505|pmid=15323743 }}</ref> In 2017, a channel capacity of 1.665 was achieved with a fidelity of 0.87 through optical fibers.<ref name="William2017">{{Cite journal |lastlast1=Williams |firstfirst1=Brian P. |last2=Sadlier |first2=Ronald J. |last3=Humble |first3=Travis S. |date=2017-02-01 |title=Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.050501 |journal=Physical Review Letters |volume=118 |issue=5 |pages=050501 |doi=10.1103/PhysRevLett.118.050501|pmid=28211745 |arxiv=1609.00713 }}Williams, B. P., Sadlier, R. J., & Humble, T. S. (2017). Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements. Physical Review Letters, 118(5).</ref> High-dimensional [[ququarts]] (states formed in photon pairs by non-degenerate [[spontaneous parametric down-conversion]]) were used to reach a channel capacity of 2.09 (with a limit of 2.32) with a fidelity of 0.98.<ref name="Hu2018">{{Cite journal |lastlast1=Hu |firstfirst1=Xiao-Min |last2=Guo |first2=Yu |last3=Liu |first3=Bi-Heng |last4=Huang |first4=Yun-Feng |last5=Li |first5=Chuan-Feng |last6=Guo |first6=Guang-Can |date=2018-07-06 |title=Beating the channel capacity limit for superdense coding with entangled ququarts |url=https://www.science.org/doi/10.1126/sciadv.aat9304 |journal=Science Advances |language=en |volume=4 |issue=7 |pages=eaat9304 |doi=10.1126/sciadv.aat9304 |issn=2375-2548 |pmc=6054506 |pmid=30035231}}</ref> [[Nuclear magnetic resonance]] (NMR) has also been used to share among three parties.<ref name="Wei2004">{{Cite journal |lastlast1=Wei |firstfirst1=Daxiu |last2=Yang |first2=Xiaodong |last3=Luo |first3=Jun |last4=Sun |first4=Xianping |last5=Zeng |first5=Xizhi |last6=Liu |first6=Maili |date=2004-03-01 |title=NMR experimental implementation of three-parties quantum superdense coding |url=https://link.springer.com/article/10.1007/BF02900957 |journal=Chinese Science Bulletin |language=en |volume=49 |issue=5 |pages=423–426 |doi=10.1007/BF02900957 |issn=1861-9541}}</ref>
