Robert M. Gingrich

Quantum Entanglement of Moving Bodies

We study the properties of quantum entanglement in moving frames, and show that, because spin and momentum become mixed when viewed by a moving observer, the entanglement between the spins of a pair of particles is not invariant. We give an example of a pair, fully spin entangled in the rest frame, which has its spin entanglement reduced in all other frames. Similarly, we show that there are pairs whose spin entanglement increases from zero to maximal entanglement when boosted. While spin and momentum entanglement separately are not Lorentz invariant, the joint entanglement of the wave function is.

Entangled light in moving frames

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.

Generalized quantum search with parallelism

We generalize Grovers unstructured quantum search algorithm to enable it to work with arbitrary starting superpositions and arbitrary unitary operators. We show that the generalized quantum search algorithm, when cast in a special orthonormal basis, can be understood as performing an exact rotation of a starting superposition into a target superposition. We derive a formula for the success probability of the generalized quantum search algorithm after n rounds of amplitude amplification. We then use this formula to determine the optimal strategy for a punctuated quantum search algorithm, i.e., one in which the amplitude amplified state is observed before the point of maximum success probability. On average, the optimal strategy is about 12% better than the naive use of Grovers algorithm. The speedup obtained is not dramatic but it illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. In addition, we show that a punctuated quantum algorithm that takes the same average computation time as Grovers standard algorithm only requires half the coherence time. We then extend the analysis to the case of a society of k quantum searches acting in parallel. We derive an analytic formula that connects the degree of parallelism with the expected computation time for k-parallel quantum search. The resulting parallel speedup scales as

Properties of entanglement monotones for three-qubit pure states

O(\sqrt{k}),

Reduction criterion for separability

while the minimum number of agents needed to ensure success, k, decreases as the inverse of the square of the achievable coherence time. This result has practical significance for the design of rudimentary quantum computers that are likely to have a limited coherence time.

All linear optical quantum memory based on quantum error correction.

Various parametrizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability, and behavior under measurement are looked at. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state under local unitary transformations. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in Phys. Rev. A 60, 910 (1999). A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.