We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm still has an advantage over the classical ones. We further show that this subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and Grover's algorithms we provide simple proofs that no non-trivial subproblems can be solved by these algorithms without entanglement.
The use of polarized photons in cryptography holds the promise of
secure cryptographic quantum key distribution schemes. In theory, quantum key distribution provides a key with unconditional security.
In practice, however, the implemented schemes are often operated in a regime which excludes unconditional security, or even in a regime in which insecurity can be proven. We shall describe here the basics of quantum key distribution, provide an overview of the main ideas that lead to a proof of its unconditional security, and discuss the insecurity of practical quantum key distribution to long distances. The above review will be undertaken with a special emphasis on the role of the polarization of photons. Finally, we shall briefly touch on the importance of photons and their polarization degree of freedom in recent proposals for small-scale optical quantum computing.
We propose a point to point quantum channel based on a two-color Spontaneous Parametric Down Conversion (SPDC), that may be applied
for a Quantum Key Distribution (QKD) system to gain better
security. We use one arm of the SPDC (770 nm - optimal for Si
detection) and a Si
counter at Alice's side to count the exact
number of photons in each pulse. Whenever the arm
contains exactly
one photon, the correlated photon (1550nm - optimal for fiber
transmission)
in the other arm is sent via a fiber to Bob. In the experiment we used an Ar^{+} laser of
514.5nm wavelength
and a BBO crystal to produce type-I photon pairs. We measured the spectrum of the SPDC and resolved specifically the 770 nm
wavelength. The rate of correlated
pairs (at 890-1050 nm) from our
SPDC source was compared to a non-correlated source. We
further
developed an InGaAs single photon detector based on Geiger mode
APD and achieved 10%
quantum efficiency and 5 * 10^{-3} dark
counts per 20nsec pulse at a temperature of -35
degrees Celsius.
We propose a scalable method for implementing linear optics quantum
computation using the "linked-state" approach. Our method avoids the
two-dimensional spread of errors occurring in the preparation of the
linked-state. Consequently, a proof is given for the scalability
of this modified linked-state model, and an exact expression for
the efficiency of the method is obtained. Moreover, a considerable improvement in the efficiency is achieved. The proposed method is applicable to the "cluster-state" approach as well.
Algorithmic cooling is a method devised by Boykin, Mor Rowchodhury, Vatan and Vrijen (PNAS Mar '02) for initializing NMR systems in general and NMR quantum computers in particular. The algorithm recursively employs two steps. The first is an adiabatic entropy compression of the computation qubits of the system. The second step is an isothermal heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. To allow experimental algorithmic cooling, the thermalization time of the reset qubits must be much shorter than the thermalization time of the computation qubits. We investigated the effect of the paramagnetic material Chromium Acetylacetonate on the thermalization times of computation qubits (carbons) and reset qubit (hydrogen). We report here the accomplishment of an improved ratio of the thermalization times from T1(H)/T1(C) of approximately 5 to around 15. The magnetic ions from the Chromium Acetylacetonate interact with the reset qubit reducing their thermalization time, while their effect on the less exposed computation qubits is found to be weaker. An experimental demonstrating of non adiabatic cooling by thermalization and magnetic ion is currently performed by our group based on these results.
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