Related papers: Error-correcting codes and absolutely maximally en…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy…
We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and…
In quantum error-correcting code (QECC), many quantum operations and measurements are necessary to correct errors in logical qubits. In the stabilizer formalism, which is widely used in QECC, generators $G_i (i=1,2,..)$ consist of multiples…
Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code,…
High-dimensional quantum systems offer a number of advantages in larger information capacity, stronger noise resiliency, higher improved efficiency and accuracy over the qubit systems. In quantum communication the maximally entangled states…
We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…
In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states:…
In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement…
Entanglement is a central resource in quantum information science, yet its structure in high dimensions remains notoriously difficult to characterize. One of the few general results on high-dimensional entanglement is given by peel-off…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
There has been much discussion recently regarding entanglement transformations in terms of local filtering operations and whether the optimal entanglement for an arbitrary two-qubit state could be realised. We introduce an experimentally…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…
An entangled two-mode coherent state is studied within the framework of $2\times 2$ dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is…
Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of…
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the…
If entanglement is available, the error-correcting ability of quantum codes can be increased. We show how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…