Abstract The Milburn dynamics of three non resonant ultra‐strongly coupled oscillators are resolved by using symplectic geometry. The Milburn dynamics of virtual excitations and how they affect the pairwise entanglement are looked at. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, it is shown that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, the effects of physical parameters on the redistribution of virtual excitations among the three bi‐partitions are analyzed. As a result, the violation of the monogamy of excitations is shown as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, it is emphasized that the treatment can be used to model coupled quantum circuits in real situations (with decoherence).
Abstract The Milburn dynamics of three non resonant ultra‐strongly coupled oscillators are resolved by using symplectic geometry. The Milburn dynamics of virtual excitations and how they affect the pairwise entanglement are looked at. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, it is shown that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, the effects of physical parameters on the redistribution of virtual excitations among the three bi‐partitions are analyzed. As a result, the violation of the monogamy of excitations is shown as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, it is emphasized that the treatment can be used to model coupled quantum circuits in real situations (with decoherence).
We study the effect of quantum entanglement maintained by virtual excitations in an ultrastrongly-coupled harmonic-oscillator system. Here, the quantum entanglement is caused by the counterrotating interaction terms and hence it is maintained by the virtual excitations. We obtain the analytical expression for the ground state of the system and analyze the relationship between the average excitation numbers and the ground-state entanglement. We also study the entanglement dynamics between the two oscillators in both the closed- and open-system cases. In the latter case, the quantum master equation is microscopically derived in the normal-mode representation of the coupled-oscillator system. This work will open a route to the study of quantum information processing and quantum physics based on virtual excitations.
Abstract The monogamy relation of quantum states has limited the shareability properties of quantum resources in multiparty quantum systems. It plays a vital role in information distribution and transformation over many sites in quantum communications. Here, we focus on the monogamy relations of quantum correlations in the context of three-flavor neutrino oscillations, related to the squared entanglement of formation, the squared of quantum discord and its geometric variant. The monogamy relations in terms of the squared entanglement of formation work for the electron and muon antineutrino oscillations, suggesting that the bipartite entanglement measured by squared entanglement of formation of the three-flavor neutrino system set a limitation to the sum of pairwise squared entanglement of formation. Furthermore, we found that the squared quantum discord is also monogamous in three-flavor neutrino system. As a comparison, we test the monogamy of the quantum discord in neutrino oscillations with the result that the quantum discord is not monogamous. In addition, it is found that the bipartite geometric quantum discord of three-flavor systems is equal to the sum of the pairwise geometric quantum discord, i.e., the monogamy relation for geometric quantum discord is saturated for three-flavor neutrino system. These monogamy relations of quantum correlations provide a way for studying the distribution of quantum resources in neutrino oscillations, which is of significance to explore the further applications of neutrino oscillations in quantum communications.
Correlations and entanglement in a chain of three oscillators A,B,C with \nnearest neighbour coupling is studied. Oscillators A,B and B,C are coupled \nbut there is no direct coupling between oscillators A,C. Examples with initial \nfactorizable states are considered, and the time evolution is calculated. It \nis shown that the dynamics of the tri-partite system creates correlations and \nentanglement among the three oscillators and in particular, between oscillators \nA,C which are not coupled directly. We have performed photon number \nselective and non-selective measurements on oscillator A and we investigated \ntheir effects on the correlations and entanglement. It is shown that, before \nthe measurement, the correlations between oscillators A,C can be stronger \nthan the correlations of oscillators A,B. Moreover, some entanglement witness \nshows that oscillators A,C are entangled but the oscillators A,B might \nor might not be entangled. By using quantum discord, which measures the \nquantumness of correlations, it is shown that there are quantum correlations \nbetween oscillators A,B and after the measurements in both cases of selective \nand non-selective measurements, oscillators A,B and A,C become classically \ncorrelated.
We consider a many-body system consisting of a harmonic oscillator linearly coupled to N others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the N others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the N others and these are found entangled.
A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.
Encoding the state of physical systems, the many-body wavefunction lives in a Hilbert space that conveniently offers a tensor factor to each constituent of the system. Consequentially, the wavefunction inherits structural properties such as entanglement, a new type of quantum correlation across the tensor factors. Entanglement can be quantified by forming polynomials in the wavefunction that remain invariant under local operations, which in turn naturally imply the properties we intuit about entanglement. It follows from the Tarski-Seidenberg theorem that these polynomial entanglement measures must obey polynomial constraints. It is among these constraints that the core features separating quantum correlations from classical correlations are illuminated, such as their monogamous nature. The smallest non-trivial system which exhibits entanglement monogamy tradeoffs governed by polynomial constraints is three qubits, for which we find novel constraints that are stronger than the previously known constraints, and which may as well be a complete description of three-qubit entanglement since the number of degrees of freedom matches the number of entanglement measures. A remarkable redundancy known in three qubits is that any party's total entanglement decomposes exactly into bipartite and tripartite type entanglement; we find that this behavior is merely part of the GHZ family tradition, and that any party within the n-qubit GHZ SLOCC equivalence class also has total entanglement which decomposes exactly into all k-partite type entanglements, thus providing insight into strong versions of monogamy relations. Refocusing back to tripartite systems, we then suppose arbitrarily many degrees of freedom into our subsystems, which appear to refuse all temptations of polygamy. Up to this point we have only been considering idealized isolated systems as it is known that monogamy relations aren't sensitive to the total purity, however we then find entanglement constraints which are violated by globally mixed states, ultimately suggesting that environments can enable entanglement to grow beyond what is otherwise allowed. Finally, we address the dynamical behavior of entanglement under several key interactions, and characterize the couplings according to their ability to generate entanglement.