# Buffering of Flying Qubits

Some of you may remember – I mentioned it in Portrait of an Academic Capitalist as a Young Man – that my minor as a PhD student at Cornell was Queuing. My papers that arose from the PhD thesis – in Management Science and in Queuing Systems – involved studying buffers in serial production lines that were operated using kanbans. Yes, way back, I was a lean manufacturing chap dealing with Just-in-Time (JIT) and such.

It turns out that in quantum communication also buffering plays an important role and its effects need to be better understood for designing effective networks.

Different from quantum computing where a qubit is stationary (although not always – I have seen a technology where the qubits actually move, using gradient field, and form different logic gates, dynamically, very cool stuff, no pun intended 😏), in quantum communication, the qubits are traveling – say, through an optical fiber – and so are called

flying qubits.

Decoherence of qubits is a major issue both in computing and in communication.

Buffering is inevitable, which causes waiting, and this waiting can cause further decoherence.

The primary question (Mukhya Prashna, see Quantum Queuing) is:

What amount of information can be transmitted over a quantum channel?

This is called Quantum Shannon Theory.

The noise model that is considered appropriate in this context is Generalized Amplitude Damping (GAD), which means that a qubit in state |0> can flip to state |1> with some probability, and this probability transition matrix, due to buffering in our situation, depends on waiting time, which is stochastic.

Furthermore, waiting times of consecutive qubits sent over a channel are correlated, and so this is an example of non i.i.d. waiting times.

Interleaving Quantum Shannon Theory and Queuing, we develop results with respect to achievable capacity in the important case of symmetric GAD, where the qubit states |0> and |1> are affected similarly due to noise, by constructing an induced channel — binary symmetric — that achieves it.

Of immense practical interest is that:

The maximum capacity can be achieved without entanglement in encoding and without joint measurement in decoding.

While it was previously known that such a channel exists, in theory, and that it did not need entanglement in encoding, it was not previously known that it did not need joint measurement in decoding too! You can find these (and more) results in:

Queue-channel Capacities and Generalized Amplitude Damping.

This research is in collaboration with faculty at IIT-Madras (Prabha, Physics; Avhishek and Krishna, ECE), and Vikesh, who was a post-doc with me after his PhD in Theoretical Physics at CMU, advised by Bob Griffiths, and will be joining IBM Research group at Yorktown Heights that includes Charles Bennett 😳 who is the first person I met at the IBM after-party, where I got on the invited list thanks to Davide Venturelli of NASA/USRA, in APS Boston in 2019 🤷🏽‍♂️ and could not resist taking a selfie!