In this work we describe a protocol by which one can secretly broadcast W-type state among three distant partners. This work is interesting in the sense that we introduce a new kind of local cloning operation to generate two mixed three qubit entangled states between these partners from a W-type state initially shared by them.
In this work, we investigate the problem of a secretly broadcasting of a three-qubit entangled state between two distant partners. The interesting feature of this problem is that starting from two-particle entangle states shared between two distant partners we find that the action of a local cloner on the qubits and the measurement on the machine state vector generates three-qubit entanglement between them. The broadcasting of entanglement is made secret by sending the measurement result secretly using cryptographic scheme based on orthogonal states. Further we show that this idea can be extended to generate three-particle entangled states between three distant partners.
It is known that maximally entangled Bell state and three-qubit W-type states are very useful in various quantum information processing task. Thus the problem of preparation of these type of states is very important in quantum information theory. But the factor which prohibit the generation of the above mentioned pure states shared between two and three distant partners is decoherence. When we send one qubit, from a two qubit state, through decoherence channel like amplitude damping channel, the purity of the qubit is lost and it ends up with a mixed state. Therefore it is very difficult to keep the pure maximally entangled state in a maximally entangled pure state or in an entangled state with high entanglement. In this work we have provided a method by which one can generate experimentally a maximally entangled Bell states shared between distant parties with a non-zero probability when a qubit, from a two qubit general state, passes through decoherence channel. Therefore, despite of the fact that qubit is interacting with the noisy channel, we are able to generate Bell state shared between two distant partners. Further, we have shown that it is possible to generate pure three-qubit W-type states shared between three distant partners using economical quantum cloning machine and weak-measurement based feed-forward control scheme, even though the second and third qubit is interacting with the noisy channel. Lastly, we have shown that the generated three-qubit W-type states can be used in teleporting one of the two non-orthogonal states.
In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal