Experimental bound entanglement through a Pauli channel
Sadiq Muhammad2013, Scientific Reports
Understanding the characteristics of a quantum systems when affected by noise is one of the biggest challenges for quantum technologies. The general Pauli error channel is an important lossless channel for quantum communication. In this work we consider the effects of a Pauli channel on a pure four-qubit state and simulate the Pauli channel experimentally by studying the action on polarization encoded entangled photons. When the noise channel acting on the photons is correlated, a set spanned by four orthogonal bound entangled states can be generated. We study this interesting case experimentally and demonstrate that products of Bell states can be brought into a bound entangled regime. We find states in the set of bound entangled states which experimentally violate the CHSH inequality while still possessing a positive partial transpose. C oherent superpositions and entanglement are key resources in quantum communication and computation tasks. Quantum methods and techniques rely on the preparation, transmission, processing, and detection of quantum states. But quantum states are very fragile and easily destroyed by decoherence processes due to unwanted coupling with the environment. These uncontrollable influences cause noise in the communication or errors in the outcome of a computation, and thus reduce the advantages of quantum information resources. To overcome the decoherence problem, several purification and distillation protocols have been proposed and implemented, each of them appropriate for a specific type of coupling with the environment 1-7. These protocols use local operations assisted by classical communications (LOCC). In most protocols the parties involved are distributed in separated locations, local operations is then a natural restriction since the parties involved can coordinated by classical communication the operations they will do on their own qubits. It has been shown that there is a class of noisy non-separable quantum states where no entanglement can be distilled. This entanglement class has been termed bound entanglement (BE) 8. These BE states live in the ''gray'' area between the separable (classical) and distillable non-separable (free entangled) states. One way to create such an irreversible noisy state is to start with a pure entangled state and then subject it to stochastic local actions which bring the state into the BE regime. These stochastic local actions can be modelled by an LOCC action and is considered to occur during the transmission of the qubits to the parties. In order to detect BE, one can use the positive partial transpose (PT) method 9 combined with an entanglement indicator such as the witness method. Even though BE is regarded as a weak form of entanglement, it has been shown that some BE states can maximally violate the CHSH inequality 10,11. Thus there is no hidden variable model that can be assigned to such states. Moreover, it has been shown that BE can be used as a resource in quantum communication tasks such as secret sharing, key distribution 12 , superactivation 13 , and super-additivity of channel capacity 14. BE has been demonstrated experimentally only very recently 15-19. In all these experiments, a large amount of depolarized noise was added to reach the BE regime, which prevented a violation of the CHSH inequality. From the perspective of quantum communication applications the violation of a Bell inequality is closely related to the reduction of communication complexity 20. Further experimental investigations are therefore needed to understand how noise affects quantum states and how BE-states are generated. Our objective is thus to identify those situations when the distributed states are in a BE-regime that is useful for quantum communication. In this work we focus on highly symmetric four-qubit BE states which are generated through a Pauli channel 21-23. Results Modelling the pauli quantum channel. Here we consider a lossless decoherence channel induced by an environment when pure entangled states are to be distributed. Suppose four separated parties Alice (A), Bob (B), Charlie (C), and David (D) like to share two pure bipartite entangled states among each other. The state considered here is two-Bell-state-like,
