Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise

Abstract

Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this Paper, we study quantum-communication channels in $d$-dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold which depends on the dimension of the Hilbert space $(d)$ and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy channel and show that in order to achieve Holevo limit, we must use $d$ particles with $d$ degrees of freedom. Our results show that entanglement is a useful means to enhance the mutual information. We choose a special non-maximally entangled state and show that in the quasi-classical depolarizing and quantum depolarizing channels, maximum classical capacity in the higher memory channels is given by the maximally entangled state. Hence, our results show that for high error channels in every degree of memory, maximally entangled states have better mutual information.

15 pages, 5 figures, PHYSICAL REVIEW A 75, 042301 (2007)

References in corpus (55)

• Mixed State Entanglement and Quantum Error Correction
• Entanglement of Orbital Angular Momentum States of Photons
• Decoherence Free Subspaces for Quantum Computation
• Encoding a qubit in an oscillator
• Security of quantum key distribution using d-level systems
• Noiseless Quantum Codes
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum cryptography with 3-state systems
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Classical capacity of the lossy bosonic channel: the exact solution
• Entanglement enhanced information transmission over a quantum channel with correlated noise
• Quantum Channels with Memory
• Robust polarization-based quantum key distribution over collective-noise channel
• Triggered qutrits for Quantum Communication protocols
• Quantum Encodings in Spin Systems and Harmonic Oscillators
• Quantum communication complexity protocol with two entangled qutrits
• Classical and quantum communication without a shared reference frame
• Fault-Tolerant Quantum Computation with Higher-Dimensional Systems
• Minimum output entropy of bosonic channels: a conjecture
• Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise
• Quantum key distribution for d-level systems with generalized Bell states
• Entangled states maximize the two qubit channel capacity for some Pauli channels with memory
• A quantum protocol for cheat-sensitive weak coin flipping
• Quantum channels with a finite memory
• Greenberger-Horne-Zeilinger paradoxes for many qudits
• Robust Quantum Communication Using A Polarization-Entangled Photon Pair
• Quantum entanglement enhances the capacity of bosonic channels with memory
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
• Entanglement assisted capacity of the broadband lossy channel
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Quantum Markov Channels for Qubits
• Additivity properties of a Gaussian Channel
• Bosonic Memory Channels
• Broadband channel capacities
• Minimum Renyi and Wehrl entropies at the output of bosonic channels
• Quantum entanglement and classical communication through a depolarising channel
• Exploiting entanglement in communication channels with correlated noise
• Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
• A dynamical model for quantum memory channels
• The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels
• Capacities of Quantum Channels and How to Find Them
• Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
• Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs
• On Strong Superadditivity of the Entanglement of Formation
• A Lower Bound on the Quantum Capacity of Channels with Correlated Errors
• Gaussian quantum channels
• From Classical State-Swapping to Quantum Teleportation
• Maximal output purity and capacity for asymmetric unital qudit channels
• Optimal local preparation of an arbitrary mixed state of two qubits. Closed expression for the single copy case
• Entanlement-Assisted Classical Capacity of Quantum Channels with Correlated Noise
• Equi-entangled bases in arbitrary dimensions
• Bell Gems: the Bell basis generalized
• Capacity of nonlinear bosonic systems
• Transmitting qudits through larger quantum channels