Discrimination between evolution operators

Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is demonstrated for every scenario but a special one. This discrimination between evolutions is experimentally much simpler than procedures proposed earlier based on either sequential or parallel application of the unknown unitaries. A lower bound for the orthogonalization time is proposed in terms of the properties of the two Hamiltonians.Comment: 7 pages, 2 figures, REVTe

Mixing quantum and classical mechanics and uniqueness of Planck's constant

Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf 8} 545\cite{sahoo}). We show that the tensor-product of two quantum Hamilton algebras, each characterized by a different Planck's constant is an algebra of the same type characterized by yet another Planck's constant. The algebraic structure of mixed quantum and classical systems is then analyzed by taking the limit of vanishing Planck's constant in one of the component algebras. This approach provides new insight into failures of various formalisms dealing with mixed quantum-classical systems. It shows that in the interacting mixed quantum-classical description, there can be no back-reaction of the quantum system on the classical. A natural algebraic requirement involving restriction of the tensor product of two quantum Hamilton algebras to their components proves that Planck's constant is unique.Comment: revised version accepted for publication in J.Phys.A:Math.Phy

The rise and fall of quantum and classical correlations in open-system dynamics

Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A unitarily evolving (isolated) quantum system generically develops extensive entanglement: the magnitude of the generated entanglement will increase without bounds with the effective Hilbert space dimension of the system. It is conceivable, that coupling of the interacting subsystems to local dephasing environments will restrict the generation of entanglement to such extent, that the evolving composite system may be considered as approximately disentangled. This conjecture is addressed in the context of some common models of a bipartite system with linear and nonlinear interactions and local coupling to dephasing environments. Analytical and numerical results obtained imply that the conjecture is generally false. Open dynamics of the quantum correlations is compared to the corresponding evolution of the classical correlations and a qualitative difference is found.Comment: 35 pages, 10 figures. Revised according to comments of the referees. Accepted for publication in Phys. Rev.

C++QED: An object-oriented framework for wave-function simulations of cavity QED systems

We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting quantum dynamics in general. The user is provided with a number of ``elements'', eg pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.Comment: 31 pages, 8 figures, 3 table

Temporal and Spatial Dependence of Quantum Entanglement from a Field Theory Perspective

We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance $d$. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation $d$. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on $d$. The detectors separated at those $d$ with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small $d$, the two detectors can have residual entanglement even if they initially were in a separable state, while for $d$ a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.Comment: 21 pages, 8 figures. Minor changes. Some plots are re-expressed in logarithmic negativity. No change in the overall result

Efficient simulation of quantum evolution using dynamical coarse-graining

A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution, which can be interpreted as a process of weak measurement of the distinguished observables performed on the evolving system of interest. Given that the observables are "classical" and the Hamiltonian is moderately nonlinear, the open system dynamics displays a large time-scales separation between the dephasing of the observables and the decoherence of the evolving state in the basis of the generalized coherent states (GCS), associated with the spectrum-generating algebra. The time scale separation allows the unitary dynamics of the observables to be efficiently simulated by the open-system dynamics on the intermediate time-scale.The simulation employs unraveling of the corresponding master equations into pure state evolutions, governed by the stochastic nonlinear Schroedinger equantion (sNLSE). It is proved that GCS are globally stable solutions of the sNLSE, if the Hamilonian is linear in the algebra elements.Comment: The version submitted to Phys. Rev. A, 28 pages, 3 figures, comments are very welcom

An Example of the Decoherence Approach to Quantum Dissipative Chaos

Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum versions of systems which classically exhibit {\it dissipative} chaos. Using the decoherence formalism of Gell-Mann and Hartle, I find a quantum mechanical analog of one such system, the forced damped Duffing oscillator. I demonstrate the classical limit of the system, and discuss its decoherent histories. I show that using decoherent histories, one can define not only the quantum map of an entire density operator, but can find an analog to the Poincar\'e map of the individual trajectory. Finally, I argue the usefulness of this model as an example of quantum dissipative chaos, as well as of a practical application of the decoherence formalism to an interesting problem.Comment: Standard LaTeX, 15 pages + 2 figures (uuencoded postscript), to appear in Physics Letters A, October 199

Finite-Time Disentanglement via Spontaneous Emission

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite time, and in a specific example we find the time to be given by $\ln \Big(\frac{2 +\sqrt 2}{2}\Big)$ times the usual spontaneous lifetime.Comment: revtex, 4 pages, 2 figure

Rapid state purification protocols for a Cooper pair box

We propose techniques for implementing two different rapid state purification schemes, within the constraints present in a superconducting charge qubit system. Both schemes use a continuous measurement of charge (z) measurements, and seek to minimize the time required to purify the conditional state. Our methods are designed to make the purification process relatively insensitive to rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67, 030301(R) (2003)] uses the measurement results to control bias (z) pulses so as to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90 (2006)] uses a simple feedback protocol which tightly rotates the Bloch vector about an axis almost parallel with the measurement axis. We compare the performance of these and other techniques by a number of different measures.Comment: 14 pages, 14 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review