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A general quantum noisy channel is analyzed, wherein the transmitted qubits may experience symmetry-breaking decoherence, along with memory effects. We find the optimal basis not to be fully entangled, but a combination of factorized and…
Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits…
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with $N$, the number of channel outputs that are detected jointly by the quantum joint-detection receiver…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes…
We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects all the single-qubit damping errors. We generalize this construction to a family of codes that…
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept…
Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate…
In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error…
The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterising the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical,…