Superdense coding: Difference between revisions

Revision as of 03:48, 22 June 2014

Revision as of 07:55, 24 June 2014

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In [[quantum information theory]], '''superdense coding''' is a technique used to send two bits of classical information using only one [[qubit]], with the aid of [[quantum entanglement|entanglement]].

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== Overview ==

Suppose Alice would like to send classical information to Bob using [[qubit]]s, instead of classical [[bit]]s. Alice would encode the classical information in a qubit and send it to Bob. After receiving the qubit, Bob recovers the classical information via [[Measurement in quantum mechanics|measurement]]. The question is: how much classical information can be transmitted per qubit? Since non-orthogonal [[quantum state]]s cannot be distinguished reliably, one would guess that Alice can do no better than one classical bit per qubit. [[Holevo's theorem|Holevo's theorem]] discusses this bound on efficiency. Thus there is no advantage gained in using qubits instead of classical bits. However, with the additional assumption that Alice and Bob share an [[entangled state]], two classical bits per qubit can be achieved. The term ''superdense'' refers to this doubling of efficiency.

Also, it can be proved that the maximum amount of classical information that can be sent (even while using entangled state) using one qubit is 2 bits.

== Details ==

Crucial to this procedure is the shared entangled state between Alice and Bob, and the property of entangled states that a ([[Maximally entangled state|maximally]]) entangled state can be transformed into another state via local manipulation.

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<math>

B_{00}, B_{01}, B_{10}, B_{11}

</math> are called Bell states.

Now, if Bob wants to find which classical bits did Alice wants to send he will perform the <math>CNOT</math> unitary operation followed by <math>H\otimes I</math>unitary operation on the entangled qubit.

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==References==

* C. Bennett and S.J. Wiesner. ''Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states.'' Phys. Rev. Lett., 69:2881, 1992 [http://prola.aps.org/abstract/PRL/v69/i20/p2881_1]

* Birgitta Whaley. ''Qubits, Quantum Mechanics and Computers.''[http://www-inst.eecs.berkeley.edu/~cs191/fa09/lectures/lecture6_fa09.pdf]

[[Category:Quantum information science]]

{{quantum computing}}

[[Category:Quantum information science]]