Related papers: Quantum Channel Capacity of Very Noisy Channels
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
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,…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard…
Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical…
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…
A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down conversion in the limit of large gain to…
We develop several lower bounds on the capacity of binary input symmetric output channels with synchronization errors which also suffer from other types of impairments such as substitutions, erasures, additive white Gaussian noise (AWGN)…
Two new classes of quantum channels, which we call more capable and less noisy, are introduced. The more capable class consists of channels such that the quantum capacities of the complementary channels to the environments are zero. The…
Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor…
We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized network coding operations on the source packets. We propose a channel model for the…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
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…
We consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy…
Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…