Simulation and implementation of the FiT Link layer quantum communication
protocol is in the central scrip simulation_fit_protocol.py.
A noisy quantum communication link between Alice and Bob is established
to enable the distribution of quantum frames from Alice to Bob. The
quantum frame's payload is either entanglement a.k.a. EPR(Einstein-Podolsky-Rosen)-Pairs
or superdense encoded information i.e. EPR-frame or SDC-frame. The
classical information that is superdense encoded at Alice and sent to
Bob is shown bellow and referenced as mario.
Since the generated EPR-Pairs are imperfect, i.e. they are generated by
the EPR-pair generator with a fidelity bellow the
maximum fidelity of 1. Additionaly, the half of the EPR-pair that belongs
to Bob is sent to him over a noisy quantum channel implemented as an
angle γ passed to a R-xy gate and
applied to the EPR-pair-half in distribution. Consequently, The fidelity
of a distributed EPR-pair decreases, depending on its pre-distribution
fidelity and the γ angle applied at the R-xy gate; This effect is
shown in the image bellow, where the percentual decrease of the fidelity
is characterized.
Additionaly, the γ angle effect on the generated EPR-pairs over time is visualized in the image bellow. It can be clearly seen how the fidelity of the EPR-pairs decreases depending on the applied γ angle.
When an EPR-frame is distributed, its fidelity is estimated by measuring
some EPR-pairs from the payload1. This is achieved thanks to the
epr-frame length estimator and entanglement manager.
Finally, in order to prevent errors when sending superdense encoded
information from Alice to Bob, a fidelity threshold policy is endorsed.
Any distributed EPR-frame, whose estimated fidelity is lower than the
decided threshold fidelity between Alice and Bob, are discarded. This is
shown in the image bellow, where the distributed EPR-pairs over time are
characterized by its fidelity and the estimated fideliety for different
EPR-frames is shown clearly diferentiating between acknowledged and
negative acknowledged EPR-frames.
To depict the consequences of setting a fidelity threshold for the distributed EPR-frames, the images bellow shows the receiped mario with and without threshold. It is clear that a threshold policy on the distributed EPR-frames minimizes the amount of errors when the distributed entanglement is later used to convei information.
| Without Threshold | Fthres = 0.9 |
|---|---|
 |
 |
The FiT protocol is inspired by the classical acknowledgement protocols
where the recipient of a data packet sends an ack-signal if the data packet
was correctly received, otherwise sends an nack-signal(negative acknowledgment)
requesting the data packet to be sent again.
The FiT protocol has two posible quantum-frames to be sended from Alice
to Bob. It can be either an EPR-frame or a SDC-frame. They are procesed
thanks to the developed entanglement manager, which
keeps track of the distributed EPR-frames and their position in the
quantum memory. I.e. in the table bellow is shown an abstraction of a
quantum memory, where the qubits of different EPR-frames are stored.
Each stored qubit has an unique qubit identifier which is used to keep
access to it. On the rigth side of the table, is shown an abstraction of
the entanglement manager. For each distributed EPR-frame, an identifier
is used (a numbers from 0, 1, 2, ...) and the estimated fidelity as well as
the qubit-identifiers of the qubits composing the EPR-frame are stored.
With this information, the entanglement manager can access specific
EPR-frames and its information in order to perform actions on them.
| Quantum Memory | Entanglement manager |
|---|---|
 |
 |
When an EPR-frame is distributed, it can be stored or dropped, depending
on its estimated fidelity and the fidelity threshold governing the protocol.
Furthermore, the specific EPR-Feedback as well as EPR-ACK/NACK are
sended between Alice and Bob to fullfil the protocol. This is shown in
the diagram bellow, where the lilac rentangles are functions implemented
in the entanglement manager.
When an EPR-frame is mistakenly received as an SDC-frame at Bob, he knows
about the mistake because of the amount of qubits in the payload. Then
he reacts accordingly as shown in the image bellow.
On the other hand, when an SDC-frame is distributed and correctly
interpreted, the information is just decoded without the need of any
feedback signal between Alice and Bob as it is shown in the image bellow.
Finally, when an SDC-frame is distributed from Alice to Bob and is
interpreted as an EPR-frame; Bob knows about the mistake because of
the payload's length. Thus he can correct the error without further
feedback signal between Alice and Bob. This is shown in the image bellow.
In order to run this simulation, a modified version of QuNetSim must be installed and is found in https://github.com/lealexis/QuNetSim.
Footnotes
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Axel Dahlberg, Matthew Skrzypczyk, Tim Coopmans, Leon Wubben, Filip Rozpędek, Matteo Pompili, Arian Stolk, Przemysław Pawełczak, Robert Knegjens, Julio de Oliveira Filho, Ronald Hanson, and Stephanie Wehner. 2019. A link layer protocol for quantum networks. In Proceedings of the ACM Special Interest Group on Data Communication (SIGCOMM '19). Association for Computing Machinery, New York, NY, USA, 159–173. https://doi.org/10.1145/3341302.3342070 ↩