Related papers: Quantum State Compression with Polar Codes
Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
The `no communication' theorem prohibits superluminal communication by showing that any measurement by Alice on an entangled system cannot change the reduced density matrix of Bob's state, and hence the expectation value of any measurement…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate…
When the 4-state or the 6-state protocol of quantum cryptography is carried out on a noisy (i.e. realistic) quantum channel, then the raw key has to be processed to reduce the information of an adversary Eve down to an arbitrarily low…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
We suggest a method for teleporting an unknown quantum state. In this method the sender Alice first uses a Controlled-Not operation on the particle in the unknown quantum state and an ancillary particle which she wants to send to the…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Entanglement distillation is a well-studied problem in quantum information, where one typically starts with $n$ noisy Bell pairs and distills $k$ Bell pairs of higher fidelity. While distilling Bell pairs is the canonical setting, it is…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schr{\"o}dinger, has also recently received much…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $\rho$ drawn from a known ensemble (but without knowing what $\rho$ is), and she transmits sufficient quantum data to a receiver Bob so that he…
Blind quantum computation is a new secure quantum computing protocol which enables Alice who does not have sufficient quantum technology to delegate her quantum computation to Bob who has a fully-fledged quantum computer in such a way that…
The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error…