Pattern-Based Quantum Key Distribution using Five- Qubit Error Correction code for Eavesdropper Detection

Abhishek Parakh, Joel van Brandwijk

Qubits traveling through a quantum channel often interact with the environment which causes errors at the receiving end. These errors are often indistinguishable from errors caused by an eavesdropper and therefore must be corrected before a quantum key exchange protocol proceeds forward. Logical qubits are often used in order to make error correction possible. In this paper, we apply logical qubits to detect collective rotational errors and discuss how they can be corrected in the context of three-stage quantum key distribution protocol.

Akihiro Yamamura, Hirokazu Ishizuka

Bilal Shaw

In the current thesis we first talk about the six-qubit quantum error-correcting code and show its connections to entanglement-assisted error-correcting coding theory and then to subsystem codes. This code bridges the gap between the five-qubit (perfect) and Steane codes. We discuss two methods to encode one qubit into six physical qubits. Each of the two examples corrects an arbitrary single-qubit error. The first example is a degenerate six-qubit quantum error-correcting code. We prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender (Alice) and the receiver (Bob) and corrects an arbitrary single-qubit error. In the second half of this thesis we explore the yet uncharted and relatively undiscovered area of quantum steganography. Steganography is the process of hiding secret information by embedding it in an innocent message. We present protocols for hiding quantum information in a codeword of a quantum error-correcting code passing through a channel. Using either a shared classical secret key or shared entanglement Alice disguises her information as errors in the channel. Bob can retrieve the hidden information, but an eavesdropper (Eve) with the power to monitor the channel, but without the secret key, cannot distinguish the message from channel noise. We analyze how difficult it is for Eve to detect the presence of secret messages, and estimate rates of steganographic communication and secret key consumption for certain protocols.

Igor M. Arbekov

Hasnaa Hajji, M. El Baz, Walter O. Krawec

Christopher John Stevens, Ben Allen, Anthony Keith Brown

We propose a method by which two radio frequency (RF) communication terminals exchange encryption keys or other data securely. This method draws on the approach developed for quantum key distribution (QKD) for detecting eavesdroppers but our method does not use any quantum properties at all. Instead, by exploiting the effects an eavesdropper has on channel stability, we explore a line-of-sight link radio in which data transfer rates are so high as to approach the Shannon limit. With very steep rises in bit error rate accompanying a small degradation of signal-to-noise limits for certain forward error correction codes, it becomes possible to infer the existence of an eavesdropper before they are able to obtain a complete key. We describe our method and analyse one possible implementation using low density parity check codes with quadrature phase shift keying modulation. The proposed technique is in principle far easier to implement than quantum-based approaches for RF and optical wireless links since the required hardware is readily available and the basic principles are well known and well understood. Finally, we show our method to have a higher key rate and spectral efficiency than those of QKD.