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The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…

Quantum Physics · Physics 2015-06-26 Mitsuru Hamada

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

Quantum Physics · Physics 2025-01-10 Lane G. Gunderman

We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…

Quantum Physics · Physics 2019-05-06 Xin Wang , Kun Fang , Runyao Duan

In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…

Quantum Physics · Physics 2025-08-14 Sujeet Bhalerao , Felix Leditzky

Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…

Quantum Physics · Physics 2016-11-29 Nicolas Delfosse , Gilles Zémor

Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…

Quantum Physics · Physics 2022-03-25 Zhengzhong Yi , Zhipeng Liang , Xuan Wang

Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…

Quantum Physics · Physics 2024-04-15 Paula Belzig , Matthias Christandl , Alexander Müller-Hermes

We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying…

Quantum Physics · Physics 2016-01-01 William Matthews , Stephanie Wehner

In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters.…

Information Theory · Computer Science 2024-05-07 Behrooz Mosallaei , Farzaneh Ghanbari , Sepideh Farivar , Vahid Nourozi

Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…

Quantum Physics · Physics 2007-06-26 Andrew S. Fletcher

The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is…

Quantum Physics · Physics 2010-07-28 Xiao-yu Chen , Li-zhen Jiang

Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…

Quantum Physics · Physics 2024-10-17 Luis Colmenarez , Ze-Min Huang , Sebastian Diehl , Markus Müller

We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…

Quantum Physics · Physics 2021-10-26 Xin Wang

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain…

Quantum Physics · Physics 2009-10-30 Seth Lloyd

We obtain a lower bound on the maximum number of qubits, $Q^{n, \epsilon}(\mathcal{N})$, which can be transmitted over $n$ uses of a quantum channel $\mathcal{N}$, for a given non-zero error threshold $\epsilon$. To obtain our result, we…

Quantum Physics · Physics 2024-12-31 Salman Beigi , Nilanjana Datta , Felix Leditzky

Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…

Quantum Physics · Physics 2008-02-03 Peter W. Shor , John A. Smolin

The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known.…

Quantum Physics · Physics 2011-03-31 Markus Grassl , Zhengfeng Ji , Zhaohui Wei , Bei Zeng

We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…

Quantum Physics · Physics 2018-07-16 Xin Wang , Wei Xie , Runyao Duan

High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…

Quantum Physics · Physics 2025-09-22 Naoyuki Kanomata , Hayato Goto