# Speed of Quantum Teleportation? [duplicate]

Is Quantum Teleportation limited by distance/time/speed?

In the classical world, the travel of information is limited by the speed of light. So I'm wondering: is there a time delay if we send information with Quantum Teleportation?

• By teleportation, do you mean to say entanglement, as teleportation is Star Trek technology, whereas entanglement is today's experimental technique. – user108787 Sep 28 '16 at 2:50
• Note: light going down fibre optic cables is actually slowed down by ~30%. So that's a bad example of "max speed". – Craig Gidney Sep 28 '16 at 3:58
• Possible duplicate of Quantum teleportation and no-communication theorem – Norbert Schuch Sep 28 '16 at 6:28
• I don't think there will ever be a month when this question is not being asked. :-/ – Norbert Schuch Sep 28 '16 at 6:30
• what is the angel speed over clouds ? – user46925 Sep 28 '16 at 12:06

Quantum teleportation requires sending classical information. So you can't do it faster than the speed of light.

Quantum Teleportation (simplified)

Alice and Bob have a pair of qubits, $A$ and $B$. $A$ and $B$ are entangled so that:

• If you measure $A$ along the X axis and also measure $B$ along the X axis, the answer will be the same.
• If you measure $A$ along the Z axis and also measure $B$ along the Z axis, the answer will be the same.

In other words, their X-parity is SAME and their Z-parity is also SAME.

Alice wants to give Bob a qubit $Q$. To do this she will compare $Q$ to $A$ along the X and Z axes, then tell Bob how the comparison went. Because $A$ and $B$ were SAME along those axes, she ends up telling Bob how to change $B$ to get $Q$.

Alice starts by measuring the X-parity of $Q$ and $A$. She finds out if they are SAME-X or DIFFERENT-X. Because $A$ and $B$ agreed along the X axis, she's actually finding out if $B$ and $Q$ agree along the X axis. If they're different-X, she yells out "HEY BOB! THE X-PARITY IS WRONG. FLIP $B$ OVER TO FIX THAT!". If $A$ and $Q$ agree along the X axis, she instead yells "X AXIS OKAY!".

Then Alice does the same thing with the Z-parity. She compares $Q$ and $A$ along the Z axis, which is actually telling her whether $B$ agrees or disagrees with $Q$ along Z. If they differ, she yells out "BOB! THE Z-PARITY IS WRONG. FLIP $B$ OVER THE OTHER WAY TO FIX THAT!". Otherwise she yells out "Z AXIS OKAY!".

After Bob hears both of Alice's yells, and has fixed any wrong parities, $B$'s state has been overwritten with $Q$'s original state. It's literally the quantum equivalent of a one-time pad cipher. (Well, except that $Q$ and $A$ get totally trashed by the measurements that Alice did.)

Notice that the process required yelling. Bob had to be told which corrections to apply. That's why quantum teleportation can't be done faster than light speed. Yells don't move faster than light.

• I thought the point of Quantum was there is no yelling, and they magically change their state in Spooky action, am I missing something ? – user982438 Sep 28 '16 at 3:42
• @user982438 Na, quantum teleportation requires the yelling. You're probably thinking of Bell test experiments. But even those don't require faster-than-light effects. Bell tests require something weird, but there's lots of possible weird to choose from. – Craig Gidney Sep 28 '16 at 3:46
• Just a few notes on the previous answer. For teleportation with photons the joint measurement on Q (the photon with the state to be teleported) and A (the member of the entangled pair held by Alice) is typically done with a simple beamsplitter followed by detectors. The has probabilistic outcomes which essentially means that it will not always provide a conclusive result that will allow Alice to tell Bob, which transformation to make. Since the detection destroys the photons there is also no way to repeat the measurement. Bottom line is that with the simplest setup the teleportation only succe – user131467 Sep 28 '16 at 5:53
• Actually it is 1/4 of the times since there are 4 possible Bell states and the Hong-Ou-Mandel process (the beam splitter method) can only measure one of them. But if it succeeds then one does not need to change the final state. – flippiefanus Sep 28 '16 at 7:09

There is no faster than light communication or motion in quantum mechanics. Teleportation does not feature any faster than light information transfer. This is a misunderstanding that is common even among physicists.

In classical physics, a system can be described by a set of numbers whose values can all be measured using a single instance of that system. There is a mathematical result called Bell's theorem saying that no local theory can reproduce the predictions of quantum mechanics using classical physics. Quantum mechanics is not classical physics and so it is not surprising that they give rise to different predictions.

In quantum mechanics, a system is characterised by the values of observables where those values are represented by mathematical objects called Hermitian matrices. To describe how information is transferred between quantum systems you have to describe the ways in which the observables of one system depend on those of another. In general, an observable does not represent just a single valued measurable quantity changing over time. Rather, it represents a more complex structure that involves multiple different versions of that quantity interfering with one another. And if there are going to be multiple versions of each system, then any given system has to carry information about how a particular version of that system will interact with a particular version of another system. In general, you can't get that sort of information by measuring just one system and for that reason it is called locally inaccessible information. An explanation of how locally inaccessible information gives rise to EPR correlations, teleportation etc by entirely local interactions is given here: