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Register a new userEntangling two oscillators with arbitrary asymmetric initial states
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A Hamiltonian is presented, which can be used to convert any asymmetric state $|varphi rangle_{a}|phi rangle_{b}$ of two oscillators $a$ and $b$ into an entangled state. Furthermore, with this Hamiltonian and local operations only, two oscillators, initially in any asymmetric initial states, can be entangled with a third oscillator. The prepared entangled states can be engineered with an arbitrary degree of entanglement. A discussion on the realization of this Hamiltonian is given. Numerical simulations show that, with current circuit QED technology, it is feasible to generate high-fidelity entangled states of two microwave optical fields, such as entangled coherent states, entangled squeezed states, entangled coherent-squeezed states, and entangled cat states. Our finding opens a new avenue for creating not only two-color or three-color entanglement of light but also wave-like or particle-like entanglement or novel wave-like and particle-like hybrid entanglement.
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We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed perfect entangler at all purities and give numerical evidence for the existence of the second one. Further, we find that there are other gates, many in fact, which are perfect entanglers for a restricted range of purities. This highlights the fact that many perfect entangler gates could in principle be found if a thorough analysis of the full parameter space is performed.
A quantum algorithm can be decomposed into a sequence consisting of single qubit and 2-qubit entangling gates. To optimize the decomposition and achieve more efficient construction of the quantum circuit, we can replace multiple 2-qubit gates with a single global entangling gate. Here, we propose and implement a scalable scheme to realize the global entangling gates on multiple $yb$ ion qubits by coupling to multiple motional modes through external fields. Such global gates require simultaneously decoupling of multiple motional modes and balancing of the coupling strengths for all the qubit-pairs at the gate time. To satisfy the complicated requirements, we develop a trapped-ion system with fully-independent control capability on each ion, and experimentally realize the global entangling gates. As examples, we utilize them to prepare the Greenberger-Horne-Zeilinger (GHZ) states in a single entangling operation, and successfully show the genuine multi-partite entanglements up to four qubits with the state fidelities over $93.4%$.
The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arbitrary joint unitary on the system and environment; the other concerned with specific initial states that may be highly entangled. Here we study the latter problem, and highlight the interplay between the initial correlations and the unitary applied. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.
The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for $c$-number observables. In addition, the interaction between pointer and object must be sufficiently weak. There is no restriction on the purity of the pointer state. For example, a thermal pointer state is fully valid.
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