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I've heard lots of talk over the past decade about the potential of quantum computing. Most of what I've read about the topic (mostly articles targeted at the layman) focuses on the exponential computational gains that will one day be achieved by linking together more and more qubits. I don't know that any of them have directly addressed how long these quantum calculations take to complete or what factors influence how long they take.

My primary reason for asking is the following thought chain:

  1. Measuring one particle in an entangled pair of particles separated by a vast distance can influence subsequent measurements made on the other particle and that influence is faster than the speed of light.
  2. Quantum entanglement cannot be used to transmit information faster than the speed of light.
  3. Quantum entanglement is a central component of quantum computing.
  4. Wait a second... Is the information processing performed by a hypothetical "distributed quantum computer" subject to classical light speed limitations?

To restate the question slightly, does the information encoded in and processed by the superposition of the entangled qubits interact with all or some of the qubits in the system during a calculation? If so, can this information be considered to be traveling between these physically separated qubits? If so, does the physical distance between qubits influence the speed of the calculation?

If the physical distance separating the qubits of a quantum computer doesn't influence the speed of the computation, how can we say that these qubits aren't passing actual, unambiguously real information back and forth faster than the speed of light?

If the physical distance does influence the speed of the computation, please just tell me so that I can stop thinking about this...

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  • $\begingroup$ The distance does make an influence. Practically when they say entanglement plays an important role in QC, they are mostly talking about the CNOT gate, and speed of light is a limiting factor in applying that gate on separated qubits. $\endgroup$ – Ali Jun 1 '18 at 6:58
  • $\begingroup$ Oh, thank goodness! That's a load off my mind. Thanks! $\endgroup$ – Thor Jun 1 '18 at 13:09
  • $\begingroup$ In general, to make use of distributed quantum computation, you also need a classical channel between the two to transmit information. The advantage you gain from quantum computation is because entanglement and superposition allow for the construction of algorithms that can do important things in fewer steps (which is what computer scientists typically mean when they refer to "complexity," which is somewhat, but not exactly, like "speed"). $\endgroup$ – probably_someone Jun 7 '18 at 20:39
  • $\begingroup$ So quantum computation requires that a classical channel between cubits exist in order to perform calculations using entanglement? And while a universal quantum computer can perform calculations of great complexity (when compared to classical computers), they are still subject both the traditional speed speed limits of this universe... That answers my question exactly. $\endgroup$ – Thor Jun 11 '18 at 15:44
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I will try to answer the bit regarding whether "information can be considered to be traveling between physically separated systems".

As you mention yourself, quantum correlations cannot be used for faster than light communication. Indeed, arguably, it is not even true that information is propagated instantaneously/FTL at all.

The usual reasoning that leads to thinking that information is transmitted faster than light when measuring one qubit entangled with another is that the measurement results at the two ends will (generally) be correlated. Say they are always positively correlated, so that if Alice measures $0$ then she is certain that Bob will also measure $0$. One can describe this situation by saying that from Alice's perspective, as soon as she measures $0$, Bob's state is also instantaneously changed to be $|0\rangle$. It would, therefore, seem that the act of Alice measuring her qubit instantaneously affected Bob's qubit.

To see that this kind of "instantaneous influence" is not really to be considered a transfer of information from one end to the other, consider the following classical example. You have two closed sacks, each one containing a single colored ball. You know that one of the balls is red and the other is green, but you don't know which one is in which sack. You open the first sack and you see a red ball. You, therefore, "instantaneously" know that the other sack contains the green ball. Does this mean that there was a FTL transfer of information between the sacks? Of course not! Correlation does not imply causation.

The quantum case is completely analogous, but instead of red/green balls, you have different quantum states. Measuring Alice's state does (in our simple case) determine Bob's quantum state, but this is still a quantum state and as such can lead to different outcomes when Bob measures in some basis. Note that this is not ad odds with nonlocality results such as Bell's theorem. Those stand, because you still cannot consider the system as "knowing in advance" the results of the measurements. The correlations are between the quantum states of Alice and Bob, non their classical measurement outcomes.

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  • $\begingroup$ Yeah, I get all that... I was asking more about how the entangled qubits in a quantum computer shared information between themselves. I think the comment above left by probably_someone answers my question pretty succinctly, though he/she didn't leave any citations :-( $\endgroup$ – Thor Jun 11 '18 at 15:47

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