Related papers: Dense Quantum Coding and a Lower Bound for 1-way Q…

We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…

A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in such a way that one can recover any bit x_i from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2…

Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…

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 investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system.…

In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted…

As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…

A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and…

We present a method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements (i.e. without complete process tomography), reconstruction of sets of conditional probabilities, and…

We study 1-way quantum finite automata (QFAs) and compare them with their classical counterparts. We show that 1-way QFAs can be very space efficient. We construct a 1-way QFAs that are quadratically smaller than any equivalent…

Let C: {0,1}^n -> {0,1}^m be a code encoding an n-bit string into an m-bit string. Such a code is called a (q, c, e) smooth code if there exists a decoding algorithm which while decoding any bit of the input, makes at most q probes on the…

Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…

Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…

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…

We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans.…

In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…

For any quantum transmission line, with smaller output dimension than its input, the number of classical symbols that can be reliably encoded is strictly suboptimal. In other words, if the channel outputs a lesser number of symbols than it…

We present a scheme to encode M extra classical bits to a dense-coded pair of photons. By tuning the delay of an entangled pair of photons to one of 2^M time-bins and then applying one of the quantum dense coding protocols, a receiver…

Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…