Related papers: How much entanglement is needed for quantum error …
It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary…
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise,…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and…
Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions).…
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…
We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation - quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the…
Recent progress in quantum information has led to the start of several large national and industrial efforts to build a quantum computer. Researchers are now working to overcome many scientific and technological challenges. The program's…
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…