Probabilistic Quantum Control Via Indirect Measurement

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability on the state space become less restrictive if unitary control operations may be supplemented by projective measurement. The present work builds on this idea, introducing the additional element of indirect measurement to achieve a kind of remote control. The target system that is to be remotely controlled is first entangled with another identical system, called the control system. The control system is then subjected to unitary transformations plus projective measurement. As anticipated by Schrodinger, such control via entanglement is necessarily probabilistic in nature. On the other hand, under appropriate conditions the remote-control scenario offers the special advantages of robustness against decoherence and a greater repertoire of unitary transformations. Simulations carried out for a two-level system demonstrate that, with optimization of control parameters, a substantial gain in the population of reachable states can be realized.Comment: 9 pages, 2 figures; typos added, reference added, reference remove

Representation of entanglement by negative quasi-probabilities

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.Comment: 9 pages, 2 figures; An optimization procedure for the quasi-probabilities has been adde

Necessary and sufficient conditions for bipartite entanglement

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary Hermitian operators, which makes them useful for applications in experiments. The needed optimization procedure is based on a separability eigenvalue problem, whose analytical solutions are derived for a special class of projection operators. For general Hermitian operators, a numerical implementation of entanglement tests is proposed. It is also shown how to identify bound entangled states with positive partial transposition.Comment: 7 pages, 2 figur

Characterization of two-qubit perfect entanglers

Here we consider perfect entanglers from another perspective. It is shown that there are some {\em special} perfect entanglers which can maximally entangle a {\em full} product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as {\textsc{cnot}} and {\textsc{dcnot}}, but {\em not} {\small{\sqrt{\rm{\textsc{swap}}}}}. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value, 2/9, are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such these gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.Comment: 6 pages, 1 eps figur

Maximal entanglement of two spinor Bose-Einstein condensates

Starting with two weakly-coupled anti-ferromagnetic spinor condensates, we show that by changing the sign of the coefficient of the spin interaction, $U_{2}$, via an optically-induced Feshbach resonance one can create an entangled state consisting of two anti-correlated ferromagnetic condensates. This state is maximally entangled and a generalization of the Bell state from two anti-correlated spin-1/2 particles to two anti-correlated spin$-N/2$ atomic samples, where $N$ is the total number of atoms.Comment: 5 pages, 3 figures, accepted for publication in PR

Right-veering diffeomorphisms of compact surfaces with boundary II

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group B_n on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Ro1,Ro2].Comment: 25 pages, 5 figure

Optimum unambiguous discrimination of two mixed states and application to a class of similar states

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators, and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by $\rho_2= U\rho_1 U^{\dag}$, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.Comment: 8 pages, changes in title and presentatio

Attaining subclassical metrology in lossy systems with entangled coherent states

Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust subclassical measurements [J. Joo et al., Phys. Rev. Lett. 107, 083601 (2011)]. Up to now no read-out scheme has been devised that exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss.We show substantial improvements over unentangled classical states and highly entangled NOON states for a wide range of loss values, elevating quantum metrology to a realizable technology in the near future

Decoherence induced by a dynamic spin environment (II): Disentanglement by local system-environment interactions

This article studies the decoherence induced on a system of two qubits by local interactions with a spin chain with nontrivial internal dynamics (governed by an XY Hamiltonian). Special attention is payed to the transition between two limits: one in which both qubits interact with the same site of the chain and another one where they interact with distant sites. The two cases exhibit different behaviours in the weak and strong coupling regimes: when the coupling is weak it is found that decoherence tends to decrease with distance, while for strong coupling the result is the opposite. Also, in the weak coupling case, the long distance limit is rapidly reached, while for strong coupling there is clear evidence of an expected effect: environment-induced interactions between the qubits of the system. A consequence of this is the appearance of quasiperiodic events that can be interpreted as ``sudden deaths'' and ``sudden revivals'' of the entanglement between the qubits, with a time scale related to the distance between them.Comment: 10 pages, 9 figure

Quantum quench dynamics of the Bose-Hubbard model at finite temperatures

We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength $U$ suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of $U$, it does equilibrate or relax well in a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decoherenced density matrix, a second quench is considered. It turns out that the answer is affirmative or negative according to the intermediate value of $U$ is zero or not.Comment: preprint, 20 pages, 7 figure