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Workshop on Recent Advances in Photonics (WRAP)

Entanglement and its role on the capacity of noisy two-Pauli channels

Ankur Raina, Shayan Garani Srinivasa

Published Dec 1, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1109/wrap.2015.7805959

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Coherent Communication with Noisy Resources

Mark M. Wilde

This chapter demonstrates the power of both coherent communication from Chapter 7 and the particular protocol for entanglement-assisted classical coding from the previous chapter. Recall that coherent dense coding is a version of the dense coding protocol in which the sender and receiver perform all of its steps coherently. Since our protocol for entanglement-assisted classical coding from the previous chapter is really just a glorified dense coding protocol, the sender and receiver can perform each of its steps coherently, generating a protocol for entanglement-assisted coherent coding. Then, by exploiting the fact that two coherent bits are equivalent to a qubit and an ebit, we obtain a protocol for entanglement-assisted quantum coding that consumes far less entanglement than a naive strategy would in order to accomplish this task. We next combine this entanglement-assisted quantum coding protocol with entanglement distribution (Section 6.2.1) and obtain a protocol for which the channel's coherent information (Section 12.5) is an achievable rate for quantum communication. This sequence of steps demonstrates an alternate proof of the direct part of the quantum channel coding theorem stated in Chapter 23. Entanglement-assisted classical communication is one generalization of superdense coding, in which the noiseless qubit channel becomes an arbitrary noisy quantum channel while the noiseless ebits remain noiseless. Another generalization of super-dense coding is a protocol named noisy super-dense coding , in which the shared entanglement becomes a shared noisy state ρ AB and the noiseless qubit channels remain noiseless.

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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 dense coding is considered to be one of the most remarkable demonstrations of the existence of quantum entanglement. In this paper, we analyze the role of correlations (both classical and quantum) in quantum communication protocols. We study how the capacity of a single-qubit quantum channel depends on correlations between Alice and Bob. In particular, we consider a scenario when Alice and Bob share a pair of qubits in a state such that Alice's qubit is in the state described by the density operator $\ensuremath{\varrho}=\frac{1}{2}1+\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}.$ We evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice, and (2) in the case when he utilizes correlations that have been established prior to the communication. We present a simple classical scenario which might serve as a prototype of quantum dense coding. We generalize our results also for qudits. In addition, we address some aspects of the issue of security in correlation-assisted communication protocols.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.
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.
This chapter demonstrates the power of both coherent communication from Chapter 7 and the particular protocol for entanglement-assisted classical coding from the previous chapter. Recall that coherent dense coding is a version of the dense coding protocol in which the sender and receiver perform all of its steps coherently.1 Since our protocol for entanglement-assisted classical coding from the previous chapter is really just a glorified dense coding protocol, the sender and receiver can perform each of its steps coherently, generating a protocol for entanglement-assisted coherent coding. Then, by exploiting the fact that two coherent bits are equivalent to a qubit and an ebit, we obtain a protocol for entanglement-assisted quantum coding that consumes far less entanglement than a naive strategy would in order to accomplish this task. We next combine this entanglement-assisted quantum coding protocol with entanglement distribution (Section 6.2.1) and obtain a protocol for quantum communication at a rate equal to the channel's coherent information (Section 13.5). This sequence of steps demonstrates an alternate proof of the direct part of the quantum capacity theorem stated in Chapter 24. Entanglement-assisted classical communication is one generalization of superdense coding, in which the noiseless qubit channel becomes an arbitrary noisy quantum channel while the noiseless ebits remain noiseless. Another generalization of super-dense coding is a protocol named noisy super-dense coding , in which the shared entanglement becomes a shared noisy state ρ AB and the noiseless qubit channels remain noiseless. Interestingly, the protocol that we employ in this chapter for noisy super-dense coding is essentially equivalent to the protocol from the previous chapter for entanglement-assisted classical communication, with some slight modifications to account for the different setting. We can also construct a coherent version of noisy super-dense coding, leading to a protocol that we name coherent state transfer . Coherent state transfer accomplishes not only the task of generating coherent communication between Alice and Bob, but it also allows Alice to transfer her share of the state ρ AB to Bob.
This chapter demonstrates the power of both coherent communication from Chapter 7 and the particular protocol for entanglement-assisted classical coding from the previous chapter. Recall that coherent dense coding is a version of the dense coding protocol in which the sender and receiver perform all of its steps coherently. Since our protocol for entanglement-assisted classical coding from the previous chapter is really just a glorified dense coding protocol, the sender and receiver can perform each of its steps coherently, generating a protocol for entanglement-assisted coherent coding. Then, by exploiting the fact that two coherent bits are equivalent to a qubit and an ebit, we obtain a protocol for entanglement-assisted quantum coding that consumes far less entanglement than a naive strategy would in order to accomplish this task. We next combine this entanglement-assisted quantum coding protocol with entanglement distribution (Section 6.2.1) and obtain a protocol for which the channel's coherent information (Section 12.5) is an achievable rate for quantum communication. This sequence of steps demonstrates an alternate proof of the direct part of the quantum channel coding theorem stated in Chapter 23. Entanglement-assisted classical communication is one generalization of superdense coding, in which the noiseless qubit channel becomes an arbitrary noisy quantum channel while the noiseless ebits remain noiseless. Another generalization of super-dense coding is a protocol named noisy super-dense coding , in which the shared entanglement becomes a shared noisy state ρ AB and the noiseless qubit channels remain noiseless.