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[[File:Superdense coding.png|right|frame|When the sender and receiver share a Bell state, two classical bits can be packed into one qubit. In the diagram, lines carry [[qubit]]s, while the doubled lines carry classic [[bit]]s. The variables b<sub>1</sub> and b<sub>2</sub> are classic boolean, and the zeroes at the left hand side represent the pure [[quantum state]] <math>|0\rangle</math>. See the section named "[[Superdense coding#The protocol|The protocol]]" below for more details regarding this picture.]]
In [[quantum information theory]], '''superdense coding''' (oralso referred to as ''dense coding'') is a [[quantum communication]] protocol to transmitcommunicate twoa number of classical bits of information (i.e.,by eitheronly 00,transmitting 01,a 10smaller ornumber 11)of fromqubits, aunder the assumption of sender (and received pre-sharing an entangled resource. In its simplest form, the protocol involves two parties, often calledreferred to as [[Alice and Bob|Alice]]) toin athis receivercontext, (oftenwhich calledshare Bob),a bypair sendingof onlymaximally oneentangled [[qubit]]qubits, fromand allows Alice to Bob,transmit undertwo thebits assumption(''i.e.'', one of Alice00, and01, 10 or 11) to Bob pre-sharingby ansending entangledonly stateone [[qubit]].<ref name="bennett1992communication">{{cite journal|last1=Bennett|first1=C.|last2=Wiesner|first2=S.|year=1992|title=Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states|journal=Physical Review Letters|volume=69|issue=20|pages=2881–2884|doi=10.1103/PhysRevLett.69.2881|pmid=10046665}}</ref><ref name="NielsenChuang2010">{{cite book|url=https://books.google.com/books?id=-s4DEy7o-a0C|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|last1=Nielsen|first1=Michael A.|last2=Chuang|first2=Isaac L.|date=9 December 2010|publisher=Cambridge University Press|isbn=978-1-139-49548-6|page=97|section=2.3 Application: superdense coding}}</ref> This protocol was first proposed by [[Charles H. Bennett (physicist)|Bennett]] and [[Stephen Wiesner|Wiesner]] in 1992 and experimentally actualized in 1996 by Mattle, Weinfurter, Kwiat and [[Anton Zeilinger|Zeilinger]] using entangled photon pairs.<ref name="NielsenChuang2010" /> By performing one of four [[quantum gate]] operations on the (entangled) qubit she possesses, Alice can prearrange the measurement Bob makes. After receiving Alice's qubit, operating on the pair and measuring both, Bob has two classical bits of information. If Alice and Bob do not already share entanglement before the protocol begins, then it is impossible to send two classical bits using 1 qubit, 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">Wang, C., Deng, F.-G., Li, Y.-S., Liu, X.-S., & Long, G. L. (2005). Quantum secure direct communication with high-dimension quantum superdense coding. Physical Review A, 71(4).</ref>
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