Reply to "Comment on `Quantum linear Boltzmann equation with finite intercollision time' ''

Hornberger and Vacchini [Phys. Rev. A82, 036101 (2010); arxiv:0907.3018] claim that the specific collisional momentum decoherence, pointed out in my recent work [Phys. Rev. A80, 064104 (2009); arXiv:0905.3908], is already described by their theory. However, I have performed a calculation whereby I disprove the authors' claim and refute their conclusion that my recent work had no advantage over theirs.Comment: 2p

Entanglement Sudden Death as an Indicator of Fidelity in a Four-Qubit Cluster State

I explore the entanglement evolution of a four qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single qubit rotation in the measurement based cluster state model of quantum computation. To do this I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement based operations) is achieved. I find that ESD does not cause a change of behavior or discontinuity in the fidelity but may indicate when the fidelity of certain states goes to .5.Comment: 8 pages, 9 figure

Efficient quantum computation of high harmonics of the Liouville density distribution

We show explicitly that high harmonics of the classical Liouville density distribution in the chaotic regime can be obtained efficiently on a quantum computer [1,2]. As was stated in [1], this provides information unaccessible for classical computer simulations, and replies to the questions raised in [3,4].Comment: revtex, 2 pages, 1 figure; related to [1] quant-ph/0101004, [2] quant-ph/0102082, [8] quant-ph/0105149, [4] quant-ph/0110019, [3] quant-ph/011002

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

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

Entanglement Sudden Death in a Quantum Memory

I explore entanglement dynamics in examples of quantum memories, decoherence free subspaces (DFS) and noiseless subsystems (NS), to determine how a complete loss of entanglement affects the ability of these techniques to protect quantum information. Using negativity and concurrence as entanglement measures, I find that in general there is no correlation between the complete loss of entanglement in the system and the fidelity of the stored quantum information. These results complement previous results in which quantum protocols not explictly based on entanglement exhibit little correlation between ESD and the accuracy of the given protocol.Comment: 6 pages, 3 composite figure

Superoperator Analysis of Entanglement in a Four-Qubit Cluster State

In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single logical qubit rotation via measurement based cluster state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single logical qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing an arbitrary single logical qubit rotation.Comment: 9 pages, 9 composite figures, presentation of results completely rewritte

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