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Allerton Conference on Communication, Control, and Computing

Quantum communication over bit flip channels using entangled bipartite and tripartite states

Ankur Raina, Shayan Garani Srinivasa

Published Sep 1, 2014• 5 citations
Publisher

Abstract

Super dense coding is a well known protocol to communicate two classical bits using a pre-shared pair of entangled qubits. We consider the case of quantum communication over the noisy bit flip channel with a shared Bell pair and show that the encoding scheme is perfectly secure. We extend the idea of super dense coding to a tripartite system and derive expressions for Holevo capacity and accessible information for various communication scenarios among the node links.

DOI
10.1109/allerton.2014.7028615

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Super dense coding is a well known protocol to communicate two classical bits using a pre-shared pair of entangled qubits. We consider the case of quantum communication over the noisy bit flip channel with a shared Bell pair and show that the encoding scheme is perfectly secure. We extend the idea of super dense coding to a tripartite system and derive expressions for Holevo capacity and accessible information for various communication scenarios among the node links.
The discovery of super dense coding paved the way for future quantum communications that exploit the power of entanglement. The protocol lets users communicate two classical bits using a pre-shared entangled pair of qubits called a Bell pair. However, the protocol assumes that a noiseless channel exists between end users. Moreover, perfect Bell pairs may not always be created in any experimental set up. We study the single shot communication properties of partially entangled Werner state and partially entangled pure bipartite states by considering the two-Pauli channel. The two-Pauli channel accommodates for both bit flips and phase flips that qubits may suffer during transmission. Quantification of entanglement is done via entanglement of formation and its dependence on capacity is analyzed.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding. In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
Quantum dense coding could be used to transmit two classical bits with one qubit when a maximally entangled state is shared. In realistic channels, entanglement degradation reduces the channel capacity, while bit-flip noise increases decoding errors. To address these issues, we propose a novel probabilistic controlled dense coding protocol that employs the three-qubit repetition code for error correction and an auxiliary qubit for probabilistic decoding. Moreover, this proposed scheme includes a third party to supervise the communication based on a three-qubit entanglement state. The implementation steps of our protocol are presented in detail, and numerical simulations show that it achieves higher average information than dense coding without error correction. The scheme provides a robust solution for quantum communication under noisy conditions and non-maximally entangled state.
We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli channels in an arbitrary dimension and derive the super dense coding capacity (i.e. the optimal information transfer) for some given resource states. For the qubit depolarizing channel, we also optimize the super dense coding capacity with respect to the input state. We show that, below a threshold value of the noise parameter, the super dense coding protocol is optimized by a maximally entangled initial state, while above the threshold it is optimized by a product state. Finally, we provide an example of a noisy channel where non-unitary pre-processing increases the super dense coding capacity, as compared to only unitary encoding.
Abstract Superdense coding uses entanglement as a resource to communicate classical information efficiently through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we demonstrate a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary information bits. Expressed in the eigenbasis of different Pauli operators, GHZ state is characterized by a unique parity pattern which enables us to formulate a security checking technique to ensure absolute security of the protocol. We show this method is better applicable in a scenario, where the initial information is distributed among spatially separated parties. Finally, optimizing the number of qubit(s) sent to Bob, we construct a distributed dense coding method, which completely depicts absolutely secure quantum communication between many to one party.