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arXiv:1408.3831 · International Journal of Quantum Information

Study of controlled dense coding with some discrete tripartite and quadripartite states

Sovik Roy, Biplab Ghosh

Published Jul 2, 2015• 6 citations

Abstract

The paper presents a detailed study of controlled dense coding scheme for different types of three and four-particle states. It consists of GHZ state, GHZ type states, maximal slice (MS), state, 4-particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle θ. The GHZ states as a special case of MS states, depending on parameters, have also been considered here. We have seen that tripartite W state and quadripartite W state cannot be used in controlled dense coding whereas |Wn〉ABC states can be used probabilistically. Finally, we have investigated controlled dense coding scheme for tripartite qutrit states.

DOI: 10.1142/s0219749915500331

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The paper presents a detailed study of controlled dense coding scheme for different types of three and four-particle states. It consists of GHZ state, GHZ type states, maximal slice (MS), state, 4-particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle θ. The GHZ states as a special case of MS states, depending on parameters, have also been considered here. We have seen that tripartite W state and quadripartite W state cannot be used in controlled dense coding whereas |Wn〉ABC states can be used probabilistically. Finally, we have investigated controlled dense coding scheme for tripartite qutrit states.

A scheme of controlled dense coding was proposed by using non-symmetric quantum channel in3×2×2 dimensional entangled state.The collapse of the state and entanglement between Alice and Bob were controlled by Charlie's local measurement on his particle in two dimension.Then the 3×2 dimensional non-symmetric quantum channel was controlled.It can be seen that the average amount of transmitted information of dense coding was controlled by Charlie's measurement angle.One can find that the average amount of information is more than 2 bits by using maximally entangled state in the non-symmetric quantum channel.Thus,this scheme is high-efficiency.In the case the entanglement is non-maximally,the transmitted information is determined by the measurement angle 6 and the coefficient /3 of the entangled state.

We investigate minimal control power (MCP) for controlled dense coding defined by the channel capacity. We obtain MCPs for extended three-qubit Greenberger-Horne-Zeilinger (GHZ) states and generalized three-qubit W states. Among those GHZ states, the standard GHZ state is found to maximize the MCP and so does the standard W state among the W-type states. We find the lower and upper bounds of the MCP and show for pure states that the lower bound, zero, is achieved if and only if the three-qubit state is biseparable or fully separable. The upper bound is achieved only for the standard GHZ state. Since the MCP is nonzero only when three-qubit entanglement exists, this quantity may be a good candidate to measure the degree of genuine tripartite entanglement.