<p>It follows directly from our <a href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1035117" rel="nofollow">formula for entanglement-assisted capacity</a>. An alternate proof uses the classical reverse Shannon theorem and the fact that entanglement does not increase the capacity of a noiseless classical channel. This last fact can be proved by showing that if it did, you could use entanglement to transmit information with no communication. I don't remember whether the alternate proof is in the linked reference or not.</p>

CC BY-SA 3.0
2011-07-08T23:49:17.630Z
Note that entanglement CAN increase the zero-error classical capacity of a classical channel.  As a result, it can also decrease the error probability in non-asymptotic settings.
Aram Harrow
CC BY-SA 4.0
2020-05-09T12:12:24.010Z
To say that classical channel is a specific case of the quantum channel and hence make conclusions based on a capacity formula that exists for the quantum channel is simply inaccurate. Also, in the paper cited, there is no definition of what is meant by Entanglement Assisted capacity of the classical channel. Also, their argument is on the folklore and inaccurate side.
user42263
CC BY-SA 3.0
2011-07-08T21:01:38.460Z
2011-07-08T21:01:38.460Z
Peter Shor 
<p>I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a proof of this particular feature of quantum communication? Very much appreciated.</p>

<p>Thanks.</p>

<reference-request><quantum-computing><quantum-information>
Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel
Vincent Russo
# Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel

(Asked by: username_0 on 2011-07-08)

I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a proof of this particular feature of quantum communication? Very much appreciated.

Thanks.

**Tags:** reference-request, quantum-computing, quantum-information


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## 1 answers

### Answer by username_1 on 2011-07-08. Score: 11 | Accepted answer

It follows directly from our [formula for entanglement-assisted capacity](http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1035117). An alternate proof uses the classical reverse Shannon theorem and the fact that entanglement does not increase the capacity of a noiseless classical channel. This last fact can be proved by showing that if it did, you could use entanglement to transmit information with no communication. I don't remember whether the alternate proof is in the linked reference or not.

> **Comments:**
> **username_2**: Note that entanglement CAN increase the zero-error classical capacity of a classical channel.  As a result, it can also decrease the error probability in non-asymptotic settings.  
> **username_3**: To say that classical channel is a specific case of the quantum channel and hence make conclusions based on a capacity formula that exists for the quantum channel is simply inaccurate. Also, in the paper cited, there is no definition of what is meant by Entanglement Assisted capacity of the classical channel. Also, their argument is on the folklore and inaccurate side.  

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