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DiVincenzo criteria for quantum communication mentions flying qubits:

a. The ability to interconvert stationary and flying qubits b. The ability to faithfully transmit flying qubits between specified locations

So, what exactly is a flying qubit, and how is it related to and different from a normal qubit? Please help understand more. I am undertaking Delft University's course in EdX on Quantum Internet and Quantum Computers.

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Preliminary - The DiVincenzo criteria for a 'normal' quantum computer

The DiVincenzo criteria, as originally proposed by DiVincenzo, are $5$ criteria that he originally proposed in his 2000 paper. In this paper, he proposed five criteria, which are widely considered to be the five (sufficient and necessary) criteria that any physical quantum computer should meet.

As you are doing the TUD quantum crypto course, you are familiar with the concept of a quantum internet. The five DiVincenzo criteria are not sufficient for a quantum computer including a quantum internet; they come up short in the communication part. For this, two more criteria (nr. $6$ & $7$) have been 'added'. They were not originally proposed by DiVincenzo.

The two new criteria

These two new criteria have to do with communication between different quantum computers or nodes. To exchange (quantum) information between two nodes, one needs to have a carrier of this quantum information. This is exactly what a flying qubit should be: a qubit that can be freely send from one node to the other.

The first extra criterium prescribes that the information encoded in a qubit within the quantum computer (often referred to as the stationary qubit in this context) should be reliably transfered to a flying qubit. Additionally, an obtained flying qubit's information needs to be reliably tranferred back to a stationary qubit as well.

The second extra criterium prescribes that such a flying qubit should be reliably send from one node to another. This is a daunting task if you consider that the nodes might be (geographically) very far apart ($> 50$km). The coherence of the flying qubit needs to be preserved over this scale, possibly (likely) with the use of error correction.

Properties of a flying qubit when compared to a stationary qubit

A flying qubit should, just as a stationary qubit, be able to reliably store quantum information. However, there are some important distinctions. First and foremost, flying qubits have a more restricted use case than stationary ones - they are only used to propagate the information between macroscopic distances, whereas stationary qubits are used to not only store information, but also to perform calculations with.

So to compare:

Stationary qubits need to:

  • Be able to store quantum information reliably on a timescale of $\sim ms$.

  • Perform calculations: various gates/operations need to be reliably performed on them. This includes an operation that moves/converts the information to a flying qubit.

  • Be able to be measured/read out reliably.

  • Be able to be highly entangled.

Flying qubits, however, need to:

  • Be send over macroscopic distances while keeping their encoded (quantum) information intact.
  • Be operational on a macroscopic temperature scale (i.e. about room temperature).
  • Perform only one single operation reliably: converting into stationary qubits.

  • Be able to be entangled.

Therefore, there are some important distinctions between the two. To summarize in what I believe is their defining distinctions:

  • Stationary qubits need to be reliably calculated with.
  • Flying qubits need to be reliably transmitted over macroscopic distances.

Physical implementation of a flying qubit

There exist myriad different implementations of stationary qubits that all have their advantages and disadvantages; it is still an open question what the final 'go to' stationary qubit design (if any) will be. For flying qubits, there is one clear design which is the most promosing: the photon. The photon travels very fast, and has a straightforward two-level system (namely, its polarization). Also, this polarization can be conserved at higher temperatures.

Note that it is highly unlikely that stationary and flying qubits will be based on the same physical principle or design. That is to say, stationary qubits will most likely be based on an entire different physical phenomenon than stationary qubits (e.g. Ion traps, superconducting qubits/transmons, quantum dots, other confined electron systems etc. for stationary qubits.) There are, however, design for a quantum computer (with stationary qubits) based on the use of photons; only time will tell what actual implementation of stationary and flying qubits will prevail.

Current implementations of flying qubits

As an interesting sidenote, in the context of quantum key distribution, flying qubits are used in the key distillation. However, for this protocol to work, only a subset of all possible qubit states need to be transferred (often this are the eigenstates of the $Z$ and $X$ operators). This reduces the complexity of the flying qubits. Note that for a general quantum internet this reduction needs to be omitted.

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  • $\begingroup$ Thank you for the answer, JSdJ. But, the question remains - how is it related to and different from a normal qubit ? I mean, we know that two qubits can be entangled to have identical information. If we can move one of them far apart, then we can say the information is transferred across two locations. So, is this the flying qubit (entangled and moved away)? Or, the flying qubit is entirely another entity altogether? $\endgroup$ – Amitabh Srivastava Nov 25 '19 at 3:22
  • $\begingroup$ You're welcome and thanks for the feedback. I have added some discussion on the different design goals and properties of flying and stationary qubits. $\endgroup$ – JSdJ Nov 25 '19 at 7:50
  • $\begingroup$ Also, as an unrelated remark, note that two qubits can not be entangled to possess identical information. By the no cloning theorem, information can not be copied from one qubit to the other. Therefore, when we say that we transfer information from a stationary qubit to a flying one, we really mean transfer; the information is destroyed on the stationary qubit. $\endgroup$ – JSdJ Nov 25 '19 at 7:59

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