Related papers: Quantum Secret Sharing with error correction
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
We introduce a protocol for quantum secret sharing based on reusable entangled states. The entangled state between the sender and the receiver acts only as a carrier to which data bits are entangled by the sender and disentangled from it by…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Quantum secret sharing (QSS) is the result of merging the principles of quantum mechanics with secret information sharing. It enables a sender to share a secret among receivers, and the receivers can then collectively recover the secret…
I describe a method for pasting together certain quantum error-correcting codes that correct one error to make a single larger one-error quantum code. I show how to construct codes encoding 7 qubits in 13 qubits using the method, as well as…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…
Secret sharing, in which a dealer wants to split a secret in such a way that any unauthorized subset of parties is unable to reconstruct it, plays a key role in cryptography. The security of quantum protocols for the task is guaranteed by…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N-qubit codes cannot be used for…
Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to phase noise. We experimentally demonstrate this method by distributing…
In the current thesis 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. This code bridges the gap between the…