Abstract
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.
Highlights
Superdense coding[1] is one of the simplest examples showing the power of quantum entanglement
We show that the standard GHZ state and the standard W state have maximal minimal control power (MCP) values for each class, which implies that MCP can be a candidate to capture the genuine tripartite entanglement of pure states
Before we investigate the properties of MCP, let us calculate the MCPs of certain three-qubit states such as the extended GHZ states and generalized W states[23]
Summary
Controlled dense coding and minimal control power. In the standard scenario of superdense coding[1], the sender, Alice, and the receiver, Bob, initially share a Bell state, and Alice encodes classical information by performing a local operation on her qubit and sends it to Bob. We have only two distinct values of the channel capacities with assistance because the extended GHZ states are invariant under the interchange of the first and second qubit and C(ρjik) = C(ρkij) for pure states. An interesting fact about the extended GHZ states is that Charlie’s measurement basis that maximizes the average channel capacity is always. Channel capacities with and without Charlie’s assistance and MCP for generalized GHZ states. In contrast to the case of extended GHZ states, the measurement basis that maximizes the channel capacity is {|0 , 1 }, regardless of the values of λi’s.
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