In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

arXiv:1012.5570Dec 27, 20102 citations

Quantum communication via noisy channels

Z. Shadman

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 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.

Jan 1, 20110 citations

Superdense coding in noisy environments: A quantum trajectory approach

Jin Woo Jun

Using the theory of quantum trajectories, we study the classical capacity $\mathbf{C}$ of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.Using the theory of quantum trajectories, we study the classical capacity $\mathbf{C}$ of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.

Physical Review AJun 2, 20066 citations

Quantum secret sharing with two qubit bipartite mixed states

Satyabrata Adhikari

Quantum secret sharing is one of the most important and interesting quantum information processing task. In quantum secret sharing, information is split among several parties such that only one of them is able to recover the qubit exactly provided all the other parties agree to cooperate. To achieve this task, all the parties need to share entangled state. As far as my knowledge, all the previous quantum secret sharing protocol used either pure tripartite or pure bipartite entangled state. In this work we use for the first time bipartite two qubit mixed state (formed due to noisy environment) in quantum secret sharing scheme. We further show that one party cannot extract the information without the collaboration of other party. We also study the property of the shared mixed state used in the quantum secret sharing scheme.Quantum secret sharing is one of the most important and interesting quantum information processing task. In quantum secret sharing, information is split among several parties such that only one of them is able to recover the qubit exactly provided all the other parties agree to cooperate. To achieve this task, all the parties need to share entangled state. As far as my knowledge, all the previous quantum secret sharing protocol used either pure tripartite or pure bipartite entangled state. In this work we use for the first time bipartite two qubit mixed state (formed due to noisy environment) in quantum secret sharing scheme. We further show that one party cannot extract the information without the collaboration of other party. We also study the property of the shared mixed state used in the quantum secret sharing scheme.

arXiv:1011.2868Nov 12, 20104 citations

Robustness of Hillary’s Quantum Secret Sharing Protocol under Random Telegraph Noise

E. S. Elkhouly, S. I. Ali, N. Metwally

This study investigates the feasibility of sharing a classical string via quantum protocols through channels subjected to Markovian and non-Markovian Random Telegraph Noise (RTN). The quantum secret sharing protocol is implemented using three-qubit channels based on Greenberger-Horne-Zeilinger (GHZ) and W-type states. The results indicate that the shared state can be received with a fidelity exceeding 95%. The classical coding parameter, along with the measurements performed by the sender and the controller, plays a crucial role in maximizing or minimizing the fidelity of the shared state. In the non-Markovian regime, the fidelity oscillates between its upper and lower bounds due to information backflow from the environment, whereas it exhibits a monotonic decay under Markovian conditions.This study investigates the feasibility of sharing a classical string via quantum protocols through channels subjected to Markovian and non-Markovian Random Telegraph Noise (RTN). The quantum secret sharing protocol is implemented using three-qubit channels based on Greenberger-Horne-Zeilinger (GHZ) and W-type states. The results indicate that the shared state can be received with a fidelity exceeding 95%. The classical coding parameter, along with the measurements performed by the sender and the controller, plays a crucial role in maximizing or minimizing the fidelity of the shared state. In the non-Markovian regime, the fidelity oscillates between its upper and lower bounds due to information backflow from the environment, whereas it exhibits a monotonic decay under Markovian conditions.

International Conference on Data Analytics for Business and Industry (ICDABI)Oct 29, 20250 citations

Quantum secret sharing for a multipartite system under energy dissipation

Siddhant Singh, Shivang Srivastava, Prasanta Kumar Panigrahi

We propose a protocol for multipartite secret sharing of quantum information through an \textit{amplitude damping} quantum channel. This network is, for example, of two organizations communicating with their own employees connected via classical channels locally. We consider a GHZ state distributed among four members in an asymmetric fashion where the members of a sub-party collaborate to decode the received information at their end. The target is to send two bits of information in \textit{one execution} of the protocol. Firstly, we consider an ideal channel and observe that our protocol enables decoding of a secret 2-bit information with unit probability. This is accomplished by one of the senders by the use of a globally operated \textit{quantum teleportation operator}. Secondly, we implement the same protocol in a realistic scenario under energy dissipation by the use of a parameterized \textit{amplitude damping channel} with variable noise. This noise is associated with energy dissipation and hence, loss of probability to distinguish and decode the information at the receiving end. Finally, we make this task possible through an optimization algorithm. Various channel \textit{quality measures} are also quantitatively ascertained.We propose a protocol for multipartite secret sharing of quantum information through an \textit{amplitude damping} quantum channel. This network is, for example, of two organizations communicating with their own employees connected via classical channels locally. We consider a GHZ state distributed among four members in an asymmetric fashion where the members of a sub-party collaborate to decode the received information at their end. The target is to send two bits of information in \textit{one execution} of the protocol. Firstly, we consider an ideal channel and observe that our protocol enables decoding of a secret 2-bit information with unit probability. This is accomplished by one of the senders by the use of a globally operated \textit{quantum teleportation operator}. Secondly, we implement the same protocol in a realistic scenario under energy dissipation by the use of a parameterized \textit{amplitude damping channel} with variable noise. This noise is associated with energy dissipation and hence, loss of probability to distinguish and decode the information at the receiving end. Finally, we make this task possible through an optimization algorithm. Various channel \textit{quality measures} are also quantitatively ascertained.

arXiv:1712.10219Dec 29, 20171 citation

Using the theory of quantum trajectories, we study the classical capacity

\mathbf{C}

of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.