Consider a two-qubit maximally entangled state that gets corrupted when only one of the qubits is subjected to local interaction with the environment via amplitude damping channel. We show there are situations where this corrupted state gets better by allowing the other qubit also to interact with the environment. Moreover if the corrupted state is non teleporting, then it can always be made teleporting by the same prescription i.e. by allowing the second qubit to interact with the environment. Quantum entanglement [1] is a property of composite systems by virtue of which the local subsystems exhibit certain correlations among themselves that cannot be explained in classical terms. Often termed as quantum nonlocality, the subject had been under extensive study and debate since 1935 when Einstein, Podolsky and Rosen questioned the completeness of quantum mechanics [2]. Later, in 1964 in his pioneering work John Bell [3] showed that the correlations exhibited by the local subsystems that may be far apart are inherently quantum mechanical and any model admitting the description of local hidden variables (or one may prefer to say local realism) fails to explain such correlations.
Consider a two-qubit maximally entangled state that gets corrupted when only one of the qubits is subjected to local interaction with the environment via amplitude damping channel. We show there are situations where this corrupted state gets better by allowing the other qubit also to interact with the environment. Moreover if the corrupted state is non teleporting, then it can always be made teleporting by the same prescription i.e. by allowing the second qubit to interact with the environment. Quantum entanglement [1] is a property of composite systems by virtue of which the local subsystems exhibit certain correlations among themselves that cannot be explained in classical terms. Often termed as quantum nonlocality, the subject had been under extensive study and debate since 1935 when Einstein, Podolsky and Rosen questioned the completeness of quantum mechanics [2]. Later, in 1964 in his pioneering work John Bell [3] showed that the correlations exhibited by the local subsystems that may be far apart are inherently quantum mechanical and any model admitting the description of local hidden variables (or one may prefer to say local realism) fails to explain such correlations.
Composite quantum systems exhibit non-local correlations. These counter intuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two quibt states that exhibit higher order nonlocal correlations. We find that dilapidation of nonlocal correlations in the presence of noise follow the same hierarchy, that is, higher order nonlocal correlation disappears for small strength of noise, where as lower order nonlocal correlations survive strong noisy environment. We show the results for decoherence due to amplitude damping channel on various quantum states. However, we observe that same hierarchy is followed by states undergoing decoherence due to phase damping as well as depolarizing channels.
For single-qubit teleportation, it has been shown that there is a family of two-qubit mixed states whose teleportation fidelity can be enhanced by subjecting one of the qubits to an amplitude damping channel. This is an interesting result, since noise in general degrades quantum entanglement. It is believed that this enhancement is due to an improvement in the classical correlations of the two-qubit states. Here, we consider two-qubit teleportation using a family of four-qubit mixed states as a resource. In this context, we show that one can again achieve enhancement in teleportation fidelity via dissipative interactions with the local environment. For a rather general class of input states, we find that this improvement implies an enhancement in the quantum discord of some teleported states. We conjecture that an improvement in some quantum property of the four-qubit mixed states could have resulted from the local interactions. We expect that our analysis will make an important case study for future investigations on the different aspects of composite quantum systems.
Recently, Badziag et al. [Phys. Rev. A 62, 012311 (2000)] obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via an amplitude damping channel (ADC). We show that such noisy states result while sharing the states $|{\ensuremath{\Phi}}^{\ifmmode\pm\else\textpm\fi{}}〉=1/\sqrt{2}(|00〉\ifmmode\pm\else\textpm\fi{}|11〉)$ across the ADC. We also show that under similar dissipative interactions, different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense that only the noisy entangled states constructed from the Bell states $|{\ensuremath{\Phi}}^{\ifmmode\pm\else\textpm\fi{}}〉$ can sometimes be made better by subjecting the unaffected qubit to a dissipative interaction with the environment. Importantly, if the noisy state is nonteleporting, then it can always be made teleporting with this prescription. We derive the most general restrictions on improvement of such noisy states assuming that the damping parameters are different for both qubits. However, this curious prescription does not work for the noisy entangled states generated from $|{\ensuremath{\Psi}}^{\ifmmode\pm\else\textpm\fi{}}〉=1/\sqrt{2}(|01〉\ifmmode\pm\else\textpm\fi{}|10〉).$ This shows that an a priori knowledge of the noisy channel might be helpful in order to decide which Bell state needs to be shared between Alice and Bob.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
In reality, a quantum system will inevitably interact with the environment around it, and this will lead to decoherence. In this paper, we mainly study quantum entanglement and Einstein–Podolsky–Rosen (EPR) steering of two-qubit system in some typical environments. Exactly, consider the initial two-qubit state to be the Werner-type state, we let one of the qubits pass through some different channels including amplitude damping (AD) channel, phase damping (PD) channel, phase flip (PF) channel, and bit flip (BF) channel. We research entanglement and EPR steering in the progress. Most importantly, we find that entanglement and EPR steering can be improved by local filtering operations with an appropriate k. Besides, we also give an example of the fact that the EPR steering is the proper subset of entanglement. These results will promote the application of the two quantum resources in quantum information tasks.
The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.