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What is the actual difference between quantum teleportation and quantum entanglement with dense coding.

Wikipedia says:

Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away,

and quantum entanglement as

the phenomenon in which two or more quantum particles can become correlated in such a way that their states are intrinsically linked, regardless of the distance between them.

But I still don't understand the actual difference.

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Both teleportation and (super)dense coding use entanglement as a resource. I like to think that one is dual to the other, as the quantum circuits are, basically, inverses of each other.

For example, if Alice wishes to teleport a single qubit to Bob, then as long as Alice and Bob pre-share an entangled Bell state, Alice can entangle her test qubit with one element of the pair, measure that element as well as the test qubit, and send two classical bits of information to Bob (who then applies the appropriate circuit to his element of the pair). But, if Alice wishes to send two classical bits to Bob, then she encodes the bits by applying appropriate gates to her element of the pair, and then sends the qubit to Bob (who does another entangling measurement).

Both require Alice and Bob to pre-share some fiducial Bell pair. Entanglement allows Alice to later send an arbitrary and unknown qubit to Bob using two classical bits of information over a classical channel, while superdense coding allows Alice to send two classical bits over a quantum channel.

You might also review Bennett's Laws as:

  • 1 qubit $\geq$ 1 (classical) bit,
  • 1 qubit $\geq$ 1 (element of an entangled pair) ebit,
  • 1 ebit + 1 qubit $\geq$ 2 bits (superdense coding), and
  • 1 ebit + 2 bits $\geq$ 1 qubit (teleportation).

Wikipedia says that these were formulated in 1993, before we even had the term for "qubit".

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    $\begingroup$ An extended duality perspective is also given in a recent paper $\endgroup$
    – Rammus
    Nov 11, 2023 at 16:05
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    $\begingroup$ I didn't know Bennette formalized these! $\endgroup$
    – FDGod
    Nov 12, 2023 at 9:53
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    $\begingroup$ @FDGog I’m trusting the 1993 date from the Wikipedia article - I haven’t found the primary source yet, but it does sound like something C. Bennett might say. $\endgroup$ Nov 12, 2023 at 13:16

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