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In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Permutation channels model communication and storage scenarios in which the positional identity of the physical carriers is partially or completely lost, so that the transmitted information is only accessible up to an unknown reordering.…
Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. have shown that the lower bound on the uncertainties of the measurement…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography,…
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for…
Quantum Key Distribution (QKD) is a promising technology for secure communication. Nevertheless, QKD is still treated with caution in certain contexts due to potential gaps between theoretical models and actual QKD implementations. A common…
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a…
As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…
The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels…
Given a Calderbank-Shor-Steane (CSS) code, it is sometimes necessary to modify the code by adding an arbitrary number of physical qubits and parity checks. Motivations may include concatenating codes, embedding low-density parity check…
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
Uncloneable encryption is a cryptographic primitive which encrypts a classical message into a quantum ciphertext, such that two quantum adversaries are limited in their capacity of being able to simultaneously decrypt, given the key and…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…