The final code is also posted on the git-hub(some self-written script of the project is called in that file).Īnd the quantum circuit from the reference is To access and edit the quantum circuit and view the Bloch sphere of the quantum state online, click the hyperlink(to run and see the Bloch sphere you have to sign in). Using this scheme Alice can hide up to four stego-qubits.$\newcommand$). We also provide an example of how Alice hides quantum information in the perfect code when the underlying channel between Bob and her is the depolarizing channel. 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. 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. Using either a shared classical secret key or shared entanglement Alice disguises her information as errors in the channel. We present protocols for hiding quantum information in a codeword of a quantum error-correcting code passing through a channel. Steganography is the process of hiding secret information by embedding it in an "innocent" message. In the second half of this thesis we explore the yet uncharted and relatively undiscovered area of quantum steganography. We discuss the advantages and disadvantages for each of the two codes. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. 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. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. We then 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.
#First quantum error correcting code how to#
We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We explicitly provide the stabilizer generators, encoding circuits, codewords, logical Pauli operators, and logical CNOT operator for this code.
The first example is a degenerate six-qubit quantum error-correcting code. Each of the two examples corrects an arbitrary single-qubit error. We discuss two methods to encode one qubit into six physical qubits. This code bridges the gap between the five-qubit (perfect) and Steane codes. 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. When researchers embraced the idea that we live in a world where the effects of a noisy environment cannot completely be stripped away from the operations of a quantum computer, the natural way forward was to think about importing classical coding theory into the quantum arena to give birth to quantum error-correcting codes which could help in mitigating the debilitating effects of decoherence on quantum data. Without their conception, quantum computers would be a footnote in the history of science. Quantum error-correcting codes have been the cornerstone of research in quantum information science (QIS) for more than a decade.
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