相关论文: Entanglement of Subspaces and Error Correcting Cod…
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information…
It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
We investigate the average bipartite entanglement, over all possible divisions of a multipartite system, as a useful measure of multipartite entanglement. We expose a connection between such measures and quantum-error-correcting codes by…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
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…
A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…
We introduce a new multiparty cryptographic protocol, which we call `entanglement sharing schemes', wherein a dealer retains half of a maximally-entangled bipartite state and encodes the other half into a multipartite state that is…
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…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank,…
In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the sender and the receiver have access to pre-shared entanglement. Such codes promise better information rates or improved error handling properties.…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…