Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but produces perfect clones. We also studied how to modified the setup to produce local copies.
Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but produces perfect clones. We also studied how to modified the setup to produce local copies.
Here we propose a feasible experimental setup for implementing optimal probabilistic cloning of two arbitrary nonorthogonal qubit states. This proposal is based on linear optics together with a pair of entangled twin photons generated via spontaneous parametric down-conversion. The states to be cloned are encoded in the polarization degree of freedom of one of the photons while two perfect clones are generated and encoded in the polarization and the spatial degree of freedom of the resting photon. Therefore, the clones are produced nonlocally. The proposed implementation requires the application of recovery unitary operations onto the photon hosting the clones which are conditional on measurements performed on the other photon in a process akin to quantum teleportation.
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of non-orthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D . We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D = 2, 3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D. We show that if some of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D=2,3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.
Quantum nonlocality, a form of nonclassicality, serves as a crucial resource in quantum information processing. Nonlocality in quantum systems is exemplified by the perfect discrimination of orthogonal quantum states through single joint measurements, which is unattainable using local operations and classical communication (LOCC). Bandyopadhyay [S. Bandyopadhyay, Phys. Rev. Lett. 106, 210402 (2011)] established that, with LOCC alone, at most $N\ensuremath{-}1$ copies of N orthogonal quantum states are required for perfect discrimination. Here, we present the experimental verification of orthogonal quantum state discrimination employing LOCC. Our results demonstrate that up to three copies suffice for the perfect distinction of four orthogonal two-qubit states via LOCC. The verified method of perfectly distinguishing orthogonal quantum state sets offers potential applications in quantum information processes, including quantum secret sharing and quantum teleportation.
In our work we explore the field of quantum state discrimination and quantum cloning. Recently the problem of optimal state discrimination with a Fixed Rate of Inconclusive Outcomes (FRIO strategy) has been solved for two pure quantum states and a few other highly symmetric cases. An optical implementation to FRIO for pure states is provided. The physical implementation can be carried out with the use of a six-port interferometer constructed with optical fibers beam splitters, phase shifters and mirrors. The input states are composed of qubits which are realized as photons in the dual-rail representation. The non-unitary measurements are carried out at the output for the presence or absence of a photon. The setup optimally interpolates between minimum error and unambiguous state discrimination. We also extend the FRIO strategy to two mixed states, whose eigenvectors in their spectral representation form a Jordan basis. We derive the minimum error rate PE for a fixed inconclusive rate Q and, in particular, the optimal distribution of the total Q over the Jordan subspaces. As Q is varied between the two limits, 0 < Q < Qc, a structure with multiple thresholds, Q1(th) (=0) < Q2(th) < . . . < QN(th) < Qc, emerges. We also solve the problem of state separation of two known pure states in the general case where the known states have arbitrary prior probabilities. The solution emerges from a geometric formulation of the problem. This formulation also reveals a deeper connection between cloning and state discrimination. The results are then applied in designing a scheme for hybrid cloning which interpolates between approximate and probabilistic exact cloning. It is shown that state separation and hybrid cloning are generalized schemes to well established state discrimination and cloning strategies. The connection between cloning and state separation is derived in the asymptotic limit.
An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For M>6, the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits. It is shown that this cloning transformation can be implemented probabilistically via parametric down conversion by feeding the signal and idler modes of a nonlinear crystal with orthogonally polarized photons.