International Journal of Quantum Information

We argue that the dimensionality of the space of quantum systems’ states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically-correlated states in spaces of dimension large enough. We illustrate things with some simple examples that justify our claim.

We derive a stochastic master equation (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak continuous quantum measurement. On account of that correlated environments can lead to a non-local open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.

In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.

We consider quantum information entropy phenomenon for multi-qubit Rabi system. By introducing different measurements schemes, we establish the relation between information entropy approach and Von Neumann entropy. It is shown that the information entropy is more sensitive to the time development than the Von Neumann entropy. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to population dynamics, such that more accurate dynamical results may be obtained using information entropy due to variation of the frequency detuning and the coupling constant.

We studied in this paper the bipartite quantum systems in finite Hilbert space. We applied the measurement on the first subsystem only and studied how this measurement is affecting the entropy of the second subsystem. The analytic work carried out in this paper shows that the post measurement state is factorizable when measurement is applied on the first subsystem. This result shows that the disorder of the system is reduced and hence the entropy of the whole system is reduced as expected. However, it is also shown in this work that the entropy of the second subsystem of the post-measurement state could be greater than that of the original state. Increasing entropy after measurement means that the disorder in the second subsystem is increased. The information we gain from measuring the first subsystem reduces our information about the second subsystem rather than increasing it or at least keeping it the same as expected. This means that more factors may be required in order to calculate the probability of finding the second subsystem in a certain state.

Many-qubit entanglement is crucial for quantum information processing although its exploitation is hindered by the detrimental effects of the environment surrounding the many-qubit system. It is thus of importance to study the dynamics of general multipartite non-classical correlation, including but not restricted to entanglement, under noise. We did this study for four-qubit Greenberger–Horne–Zeilinga (GHZ) state under most common noises in an experiment and found that non-classical correlation is more robust than entanglement except when it is imposed to dephasing channel. Quantum discord presents a sudden transition in its dynamics for Pauli-X and Pauli-Y noises as well as Bell-diagonal states interacting with dephasing reservoirs and it decays monotonically for Pauli-Z and isotropic noises.

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be nonoptimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work, we establish optimal uncertainty relations by characterizing the optimal lower bound in scenarios similar to the Maassen–Uffink type. We disprove a conjecture by Englert et al. and generalize various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.

Two kinds of thermal quantum correlations, measured respectively by quantum discord (QD) and the generalized negativity (GN), are studied for various magnetic fields, couplings, and temperatures in a two-qubit Heisenberg XYZ model. It is shown that QD and GN can exhibit a similar behavior in some regions of magnetic field, coupling, and temperature, while they behave in a contrary manner in other regions. For example, QD may increase with suitable magnetic fields, couplings, and temperature when GN decreases. QD is more robust against temperature than GN, and can reveal a kink at a suitable coupling at finite temperature while GN cannot. Moreover, a nearly unchanged QD or GN can be obtained in a large region of magnetic field, coupling, and temperature. These adjustable QD and GN via the varied magnetic field, coupling, and temperature may have significant applications in quantum information processing.

We have studied several ground states and their entanglement structure for a two-dimensional 5-site frustrated $J_1$–$J_2$ system in the presence and absence of an external magnetic field. We have used concurrence as a measure of bipartite entanglement and the Meyer–Wallach measure and its generalizations as the measures of multipartite entanglement. They provide a total of eight measures which lead to 30 entanglement quantities for each possible ground state. Computing these 30 quantities for several ground states, we have provided a detailed exposition of the entanglement distribution in each state. We have also categorized them into separable states, not showing entanglement for any bipartition; globally-entangled states, showing entanglement for all the bipartitions, and the states in between. It turns out that by adjusting the external magnetic field, conditioned on the values of the interaction parameters, one may generate specific ground states belonging to a specific class, appropriate for specific tasks in quantum information theory.

We study the effect of the interference between two independent non-Markovian reservoirs on the non-Markovianity of a two-level system. We find that the interference can enhance the non-Markovianity of the system. The additive master equation (ME) is invalid even if only one of the two reservoirs is non-Markovian, while it is a good approximation when all reservoirs are Markovian. We also derive the two states uniqueness for a two-level system coupled to structured reservoirs which maximize the measure of non-Markovianity defined by Breuer et al. [Phys. Rev. Lett. 103 (2009) 210401].