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{{multiple issues|{{more footnotes|date=August 2013}}
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{{Use American English|date=January 2019}}
[[File:Video superdense coding.ogg|right|thumb|Schematic video demonstrating individual steps of superdense coding. A message consisting of two bits (in video these are (1, 0)) is sent from station A to station B using only a single particle. This particle is a member of an entangled pair created by source S. Station A at first applies a properly chosen operation to its particle and then sends it to station B, which measures both particles in the Bell basis. The measurement result retrieves the two bits sent by station A.]]
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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 |last1=Wang
== Overview ==
[[File:Superdense coding.png|right|thumb|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
Suppose [[Alice and Bob|Alice]] wants to send two classical bits of information (00, 01, 10, or 11) to Bob using [[Qubit|qubits]] (instead of classical [[Bit|bits]]). To do this, an entangled state (e.g. a Bell state) is prepared using a Bell circuit or gate by Charlie, a third person. Charlie then sends one of these qubits (in the Bell state) to Alice and the other to Bob. Once Alice obtains her qubit in the entangled state, she applies a certain quantum gate to her qubit depending on which two-bit message (00, 01, 10 or 11) she wants to send to Bob. Her entangled qubit is then sent to Bob who, after applying the appropriate quantum gate and making a [[Measurement in quantum mechanics|measurement]], can retrieve the classical two-bit message. Observe that Alice does not need to communicate to Bob which gate to apply in order to obtain the correct classical bits from his projective measurement.
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:<math>|B_{10}\rangle = \frac{1}{\sqrt{2}}(|0_A0_B\rangle - |1_A1_B\rangle)</math>
4. If, instead, Alice wants to send the classical two-bit string 11 to Bob, then she applies the quantum gate <math>Z*X = iY = \begin{bmatrix} 0 &
:<math>|B_{11}\rangle = \frac{1}{\sqrt{2}}(|0_A1_B\rangle -|1_A0_B\rangle ) </math>
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== 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 |last1=Schaetz
==References==
{{reflist}}
== Further reading ==
* Wilde, Mark M., 2017, [http://www.cambridge.org/us/academic/subjects/computer-science/cryptography-cryptology-and-coding/quantum-information-theory-2nd-edition Quantum Information Theory, Cambridge University Press], Also available at [https://arxiv.org/abs/1106.1445 eprint arXiv:1106.1145]
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