Applications of atomic ensembles in distributed quantum computing

Thesis chapter. The fragility of quantum information is a fundamental constraint faced by anyone trying to build a quantum computer. A truly useful and powerful quantum computer has to be a robust and scalable machine. In the case of many qubits which may interact with the environment and their neighbors, protection against decoherence becomes quite a challenging task. The scalability and decoherence issues are the main difficulties addressed by the distributed model of quantum computation. A distributed quantum computer consists of a large quantum network of distant nodes - stationary qubits which communicate via flying qubits. Quantum information can be transferred, stored, processed and retrieved in decoherence-free fashion by nodes of a quantum network realized by an atomic medium - an atomic quantum memory. Atomic quantum memories have been developed and demonstrated experimentally in recent years. With the help of linear optics and laser pulses, one is able to manipulate quantum information stored inside an atomic quantum memory by means of electromagnetically induced transparency and associated propagation phenomena. Any quantum computation or communication necessarily involves entanglement. Therefore, one must be able to entangle distant nodes of a distributed network. In this article, we focus on the probabilistic entanglement generation procedures such as well-known DLCZ protocol. We also demonstrate theoretically a scheme based on atomic ensembles and the dipole blockade mechanism for generation of inherently distributed quantum states so-called cluster states. In the protocol, atomic ensembles serve as single qubit systems. Hence, we review single-qubit operations on qubit defined as collective states of atomic ensemble. Our entangling protocol requires nearly identical single-photon sources, one ultra-cold ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates in a single step Q-qubit GHZ states with success probability p(success) similar to eta(Q/2), where eta is the combined detection and source efficiency. This is signifcantly more efficient than any known robust probabilistic entangling operation. The GHZ states form the basic building block for universal cluster states, a resource for the one-way quantum computer

Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramer-Rao bound.Comment: 22 pages, 4 figure

Ultimate limits to quantum metrology and the meaning of the Heisenberg limit

For the last 20 years, the question of what are the fundamental capabilities of quantum precision measurements has sparked a lively debate throughout the scientific community. Typically, the ultimate limits in quantum metrology are associated with the notion of the Heisenberg limit expressed in terms of the physical resources used in the measurement procedure. Over the years, a variety of different physical resources were introduced, leading to a confusion about the meaning of the Heisenberg limit. Here, we review the mainstream definitions of the relevant resources and introduce the universal resource count, that is, the expectation value of the generator (above its ground state) of translations in the parameter we wish to estimate, that applies to all measurement strategies. This leads to the ultimate formulation of the Heisenberg limit for quantum metrology. We prove that the new limit holds for the generators of translations with an upper-bounded spectrum.Comment: 10 pages, 6 figures, Published version: some clarifications given on the applicability of the new limi

Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables

We reveal a close relationship between quantum metrology and the Deutsch-Jozsa algorithm on continuous-variable quantum systems. We develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter-estimation protocol or the Deutsch-Jozsa algorithm. The parameter-estimation part of the procedure attains the Heisenberg limit and is therefore optimal. Due to the use of approximate normalizable continuous-variable eigenstates, the Deutsch-Jozsa algorithm is probabilistic. The procedure estimates a value of an unknown parameter and solves the Deutsch-Jozsa problem without the use of any entanglement