Related papers: A Lower Bound on the Quantum Capacity of Channels …
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The…
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…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel to its quantum counterpart. The key observation that we make is that the problem of bounding below the error exponent…
We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters…
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.…
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
A fundamental quantity of interest in Shannon theory, classical or quantum, is the error exponent of a given channel $W$ and rate $R$: the constant $E(W,R)$ which governs the exponential decay of decoding error when using ever larger…
A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
Communication over a noisy quantum channel introduces errors in the transmission that must be corrected. A fundamental bound on quantum error correction is the quantum capacity, which quantifies the amount of quantum data that can be…
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…
We discuss a quantum network, in which the sender has $m_0$ outgoing channels, the receiver has $m_0$ incoming channels, each channel is of capacity $d$, each intermediate node applies invertible unitary, only $m_1$ channels are corrupted,…
It is important to study the behavior of a t-error correcting quantum code when the number of errors is greater than t, because it is likely that there are also small errors besides t large correctable errors. We give a lower bound for the…
Quantum capacity, as the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of…