Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (2000)], we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using ``Werner states'' of the form $\ensuremath{\alpha}{P}_{s}+(1\ensuremath{-}\ensuremath{\alpha})I/4,$ where ${P}_{s}$ is the projector corresponding to a singlet state and $I$ is the identity. We find that our inequality is violated, implying nonlocality, if $\ensuremath{\alpha}>1/\sqrt{2}.$ In addition, we extend Werner's local hidden variable model to simulation of teleportation with the $\ensuremath{\alpha}=\frac{1}{2}$ Werner state. Thus teleportation using this state does not involve nonlocality even though the fidelity achieved is $\frac{3}{4},$ which is greater than the ``classical limit'' of $\frac{2}{3}.$ Finally, we comment on a result of Gisin's and offer some philosophical remarks on teleportation and nonlocality generally.
Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (2000)], we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using Werner states'' of the form $\ensuremath{\alpha}{P}_{s}+(1\ensuremath{-}\ensuremath{\alpha})I/4,$ where ${P}_{s}$ is the projector corresponding to a singlet state and $I$ is the identity. We find that our inequality is violated, implying nonlocality, if $\ensuremath{\alpha}>1/\sqrt{2}.$ In addition, we extend Werner's local hidden variable model to simulation of teleportation with the $\ensuremath{\alpha}=\frac{1}{2}$ Werner state. Thus teleportation using this state does not involve nonlocality even though the fidelity achieved is $\frac{3}{4},$ which is greater than the classical limit'' of 32. Finally, we comment on a result of Gisin's and offer some philosophical remarks on teleportation and nonlocality generally.
Adopting an approach similar to that of Zukowski in quant-ph/9912029, we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using `Werner states' of the form x P + (1-x) I/4, where P is the projector corresponding to a singlet state and I is the identity. We find that our inequality is violated, implying nonlocality, if x > 1/sqrt(2). In addition, we extend Werner's local hidden variable model to simulation of teleportation with the x = 1/2 Werner state. Thus teleportation using this state does not involve nonlocality even though the fidelity achieved is 3/4 which is greater than the `classical limit' of 2/3. Finally, we comment on a result of Gisin's and offer some philosophical remarks on teleportation and nonlocality generally.
The violation of Bell’s inequality in quantum mechanics implies that there exist nonlocality and entanglement. When the density matrix of a composite system cannot be written as a convex combination of the product of the density matrices of its subsystems, we say there exists entanglement. For pure states, the existence of entanglement always leads to the violation of Bell’s inequality. However, in the case of the mixed states, there may be entanglement, but Bell's inequality is not violated and in other words, the nonlocality is not manifested. In addition to Bell's inequality, quantum teleportation is also a manifestation of nonlocality. Quantum teleportation using entangled states is more successful than quantum teleportation with separable states. Therefore, the corresponding fidelity of teleported state with the initial state (in short, the fidelity) of the former is always greater than the fidelity of the latter. In this paper, for Werner's state, we will show that in a range of the related parameter, while the CHSH inequality is violated, the fidelity, which indicates the amount of success of quantum teleportation, is lower than the upper bound of the corresponding fidelity for states that can be simulated with a local hidden variable theory. Meanwhile, we will see that for Gisin's state with hidden nonlocality, filtering, which leads to the appearance of nonlocality and more specifically leads to the violation of the CHSH inequality, also increases the fidelity.
Recently, Palazuelos presented the first example of super-activation of quantum nonlocality. More precisely, by combining several copies of a state rho admitting a local hidden variable model, it becomes possible to violate a Bell inequality, in a deterministic way. Here we show that super-activation of quantum nonlocality is in fact a rather generic phenomenon. In particular, we show that any d x d entangled state with entanglement fraction larger than 1/d can be super-activated. Remarkably this implies that all entangled states which are useful for teleportation are nonlocal resources, hence providing a direct link between teleportation and nonlocality.
The hitherto unexplored nonlocality of quantum correlations in the information transfer protocol of remote state preparation (RSP) is investigated in terms of a unified nonlocality argument formulated for teleportation as well as for two distinct RSP schemes. The argument differs only in the respective types of local measurements used in each scenario. One of the RSP schemes uses single particle projective measurements, while the other uses joint Bell-basis measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH type inequalities formulated for each of the RSP setups, while being equal to each other, also turn out to be equal to that of the corresponding Bell-CHSH type local realist inequality for teleportation, using the common resource of non-maximally entangled state. This reveals that for such a resource state, the maximum amount of extractable nonlocality of correlations involved in the transfer of information is the same for the standard teleportation protocol and the two RSP schemes considered here, thereby implying that the essential difference between teleportation and remote state preparation lies in the amount of classical information required to be exchanged between parties, and not in the nonlocality of underlying correlations.
Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e., lead to deterministic violation of Bell's inequality. Our result also extends the phenomenon of superactivation of quantum nonlocality, recently proven by C. Palazuelos [Phys. Rev. Lett. 109, 190401 (2012)], and suggests that the latter might in fact be more general than initially thought.
This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension d≥5, the Gisin-Degorre's local model for a Werner state of dimension d=2 and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them for projective measurements. Finally, we introduce the local model for POVMs of Hirsch et al. for a state constructed upon the singlet with noise, that still violates the CHSH inequality after local filters are applied, hence presenting the so-called genuine hidden nonlocality.