We study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.
We study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.
Suppose we are given an entangled pair and asked how well we can produce two entangled pairs starting from a given entangled pair using only local operations. To respond to this question, we study broadcasting of entanglement using a state-dependent quantum cloning machine as a local copier. We show that the length of the interval for probability-amplitude-squared α 2 for broadcasting of entanglement using a state-dependent cloner can be made larger than the length of the interval for probability-amplitude-squared for broadcasting entanglement using a state-independent cloner. Further we show that there exists a local state-dependent cloner which gives better quality copy (in terms of average fidelity) of an entangled pair than the local universal cloner.
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
In this work, we exhaustively investigate 1→2 local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of 1→3 broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of 1→2 optimal cloning machines and application of 1→3 optimal cloning machines. Interestingly, we show that 1→3 optimal cloner does a better job at broadcasting than the successive application of 1→2 cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.
In this work, we extensively study the problem of broadcasting of quantum correlations (QCs). This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement (QCsbE). It is quite well known from the ``no-broadcasting theorem'' that perfect broadcasting of QCs is not possible. However, it does not rule out the possibility of partial broadcasting of QCs where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with a most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner both locally and nonlocally. Unlike entanglement, we find that it is impossible to broadcast QCsbE optimally. Lastly, we generalize these results for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlations defined from the perspective of entanglement and the correlations measure which claims to go beyond entanglement.
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
We derive a tight upper bound for the fidelity of a universal $N\ensuremath{\rightarrow}M$ qubit cloner, valid for any $M\ensuremath{\ge}N$, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalize the operation of a quantum cloner to mixed and/or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind.