# Teleportation Revealed

## Abstract

**:**

## 1. Introduction

## 2. The Usual Take on Teleportation

## 3. Heisenberg-Picture Descriptors

#### 3.1. Qubit Descriptors

#### 3.2. Locality and Completeness

#### 3.3. The Action of Gates

## 4. The Heisenberg Picture of Teleportation

#### 4.1. Locally Inaccessible Information

- (i)
- A system $\mathfrak{S}$ is deemed to contain information about a parameter $\theta $ if (though not necessarily only if) the probability of some outcome of some measurement on $\mathfrak{S}$ alone depends on $\theta $;
- (ii)
- A system $\mathfrak{S}$ is deemed to contain no information about $\theta $ if there exists a complete description of $\mathfrak{S}$ that satisfies Einstein’s criterion and is independent of $\theta $.

#### 4.2. On the Classicality of the Bits

#### 4.3. Explaining the Information Transfer

## 5. Counterfactual Elements of Reality

#### The Instrumentalist Temptation

It is necessary to say a few words about a view which is sometimes expressed, the idea that a physical theory should contain no elements which do not directly correspond to observables. This position seems to be founded on the notion that the only purpose of a theory is to serve as a summary of known data, and overlooks the second major purpose, the discovery of totally new phenomena. The major motivation for this viewpoint appears to be the desire to construct perfectly “safe” theories which will never be open to contradiction. Strict adherence to such a philosophy would probably seriously stifle the progress of physics.

## 6. Conclusions

Some people may enjoy conjuring tricks without ever wanting to know how they work. Similarly, during the twentieth century, most philosophers, and many scientists, took the view that science is incapable of discovering anything about reality. Starting from empiricism, they drew the inevitable conclusion (which would nevertheless have horrified the early empiricists) that science cannot validly do more than predict the outcomes of observations, and that it should never purport to describe the reality that brings those outcomes about. This is known as instrumentalism.

## 7. Discussion

- Lev Vaidman:
- If I understand correctly, the story, your story, is about the universe. When we talk about teleportation, we talk about our world. And in the many world’s interpretation, there is a part that concerns the whole universe. It is the part of the MWI where there is no collapse. There is no collapse here, no question. But there are no many worlds. Many worlds is when I perform my measurement, I split the world. In teleportation, in every world, $\alpha $ and $\beta $ jump on Bob’s qubit, and they jump at the moment of the measurement. So there is no other explanation within the world.

- CAB:
- In the teleportation protocol, the records of the measurement eventually affect—and get entangled with—many other record-like systems, as well as many systems in the environment. In the Schrodinger picture, this leads to a wave function with four highly entangled terms, which, for all practical purposes, can no longer interact with one another via quantum interference: each term becomes autonomous. What is more, in each term, there are relative properties between systems, which give a consistent account of what resembles a quasi-classical single “world”. This is the quantum theory of Everett, the unitarily evolving universal wave function, with important analyses further developed by Zeh, Zurek, Gell-Mann, Hartle, Saunders, Wallace and others.

- Andrew Jordan:
- Let me make a critical comment. You made the claim that the bits that are transmitted between Alice and Bob by the telephone are really secretly quantum bits, and I must object to that because I think that if you claim that, then the logical consequence is that there is no such thing as classical information theory. I think you have to give up on classical information theory as a thing that exists. You say that, really, everything is quantum information theory. But there are classical bits. And we are communicating with a classical channel, and so there are classical channels. So how do you respond to that criticism?

- CAB:
- Classical information theory can still exist; however, not fundamentally. In fact, we know well how it is instantiated as a subcase of quantum information theory: a decohered state has a diagonal reduced density matrix whose numbers form a distribution, so we speak of its Shannon information. However, this misses my point. I took it as a premise that the world is quantum. A telephone is made of quantum systems. And yes, it looks like it is classical to me, but that is the program launched by Everett, namely, to understand how the quantum theory can explain the emergence of the classical.

- Simon Saunders:
- Rather similar question: I do not quite get it. The classical channel is really just telling Bob what the outcome of Alice’s Bell measurement is. There is very little information there, whereas $\alpha $ and $\beta $ encode potentially vast amounts of information. So I just don’t quite get that. Can you elaborate?

- CAB:
- The channel is indeed telling Bob what the outcome of Alice’s Bell measurement is. But it is not just doing that. Wouldn’t you grant that any sort of classical channel that we can imagine is ultimately made of quantum systems? This is not an irrelevant fact when we are trying to solve the capacity problem of teleportation. The quantum systems involved in the communication line transfer $\alpha $ and $\beta $ in a way that is locally inaccessible, resilient to decoherence and realizable in a chain reaction.

- Eric Curiel:
- I have a quite general question about the approach. How should I understand entanglement entropy in this picture? It plays a very fundamental role from condensed matter physics to black hole thermodynamics. How should I understand what seems to be the manifest non-locality of quantum mechanics that makes the efficacy of Von Neumann entanglement entropy possible?

- CAB:
- Since density matrices can be recovered from descriptors and the constant Heisenberg state, so can Von Neumann entropy. But one way to understand entanglement between systems that is more in line with the Heisenberg picture is that no observable of a subsystem has a definite outcome, while some observables on the joint system do. For instance, the preparation of $|{\Phi}^{+}\rangle $ on ${\mathfrak{Q}}_{2}$ and ${\mathfrak{Q}}_{3}$ yields the following descriptors (see Figure 3):

- Tim Maudlin:
- I have two comments of a different character. One is just coming back to this telephone. There is only one information theory; it is Shannon information. You can apply it to bits, which by definition have only two possible states, you can apply it to spin $1/2$ particles that have infinitely many possible states, given by your $\alpha $ and $\beta $. It doesn’t change information theory at all. In this protocol, all that is required to implement the protocol are two bits. That is all that is required. You may say, “Oh, but I have to send a quantum system physically because physics is quantum mechanics.” It doesn’t matter if Alice sends a note classically; of course, it has more than two states, right? She can write in cursive, or she can write this way, so what? The point is that the protocol merely demands that you resolve between four possibilities. That requires two bits of information. Period end of the story.

- CAB:
- The two comments are not of a different character: they answer one another. The primality of Shannon’s information in one’s mind makes one uncritical not only of its use in teleportation but also of the way in which the assumptions are coined in Bell’s theorem, namely, in terms of classical probability distributions. For whom the very use of classical probability distributions is not considered to be an assumption made by Bell, then indeed, the violation of Bell’s inequality at spacelike separation challenges locality. Otherwise, the violation simply dismisses the hypothesis that quantum theory can be underlain by classical probability distributions.

- David Wallace:
- I want to go back to the Deutsch–Hayden claim that once I have a local formulation of the theory, then the theory is local. The worry is that there are relatively clear cheap ways of making a theory local. I’m not claiming this is a cheap way. But there are cheap ways. For instance, I can just attach a copy of the state of the universe to every local system, I can say whatever my wildly nonlocal description is, in my new theory, the state of the system is the ordered pair of the state of the old theory and the state of the universe. It is horrendously expensive; call that a monadology move, for Leibniz’s fans. That framework is formally going to be local, but clearly, it is not telling us that the theory is interestingly local. I don’t think that the framework of descriptors has this character, although there are bits of it that sometimes worry me. But I just want to flag that a bit more needs to be done to clarify that a theory is local just because it has a local formalism. I think we have to avoid making moves of that kind.

- CAB:
- What you suggest does not fulfill Einstein’s criterion because if a state of the whole universe is included in the description of each localized system, then if Bob performs an operation on his system, it affects Alice’s description.

## Funding

## Acknowledgments

## Conflicts of Interest

## Correction Statement

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**Figure 3.**The descriptors in quantum teleportation. The computation starts with all qubits properly initialized to ${\mathit{q}}_{i}\left(0\right)$, which, for conciseness, is denoted without time dependence as $({q}_{ix},{q}_{iz})$. When entering a gate, the components of the input are shuffled into the output in accordance with the action of the gate, which is prescribed by Equations (5), (6) and (8). The information flow of the parameters $\alpha $ and $\beta $, encoded in $\overrightarrow{\phi}$, is highlighted in dark grey, with the wires thickened. It spreads locally in the network through the interactions, and, as can be seen, the “classical” bits are responsible for carrying the parameters encoding Alice’s system over to Bob’s location.

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Bédard, C.A.
Teleportation Revealed. *Quantum Rep.* **2023**, *5*, 510-525.
https://doi.org/10.3390/quantum5020034

**AMA Style**

Bédard CA.
Teleportation Revealed. *Quantum Reports*. 2023; 5(2):510-525.
https://doi.org/10.3390/quantum5020034

**Chicago/Turabian Style**

Bédard, Charles Alexandre.
2023. "Teleportation Revealed" *Quantum Reports* 5, no. 2: 510-525.
https://doi.org/10.3390/quantum5020034