[show abstract][hide abstract] ABSTRACT: Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation. Here, we implement a compiled version in a photonic system. For the first time, we demonstrate the core processes, coherent control, and resultant entangled states required in a full-scale implementation. These are necessary steps on the path towards scalable quantum computing. Our results highlight that the algorithm performance is not the same as that of the underlying quantum circuit and stress the importance of developing techniques for characterizing quantum algorithms.
[show abstract][hide abstract] ABSTRACT: We experimentally investigate nonlinear couplings between vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.
[show abstract][hide abstract] ABSTRACT: We study quantum statistics of optical fields in the far zone of a light source consisting of a number of uncorrelated atoms. The quantum statistics of such a system can be universal under certain conditions.
Quantum Electronics and Laser Science Conference, 2005. QELS '05; 06/2005
[show abstract][hide abstract] ABSTRACT: The teleportation of an atomic state accomplishes the complete transfer of information from one particle to another, employing the non-local properties of quantum mechanics. Recently, two groups have achieved the deterministic teleportation of a quantum state between a pair of trapped ions. Following closely the original proposal of Bennett et al., a highly entangled pair of ions is created, a complete Bell-state projective measurement involving the source ion and one of the entangled pair is carried out, and state reconstruction conditioned on this measurement is performed on the other half of the entangled pair.
[show abstract][hide abstract] ABSTRACT: Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: Scheme I requires several sets of crystals, while Scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states. Comment: 11 pages, 6 figures, accepted by PRA
[show abstract][hide abstract] ABSTRACT: Three Ca-40 ions trapped in a linear Paul trap serve as a three-qubit register that can be manipulated by series of suitably tailored laser pulses. We implement deterministic quantum teleportation in the following way: First, we create a maximally entangled pair of ions that will be shared between the sending and the receiving party. Next, the third quantum bit is prepared in an arbitrary quantum state that will be teleported to the quantum bit of the receiver (the target). This is done by measuring the quantum bits of the sender in a basis of maximally entangled states and depending on the measurement result - applying one out of four unitary transformations to the target qubit. This teleportation protocol can be completely characterized by preparing six different input states and tomographically reconstructing the corresponding output states. The information obtained in this way is used for reconstructing the quantum process with the help of a maximum-likelihood technique.
[show abstract][hide abstract] ABSTRACT: We demonstrate complete characterization of a two-qubit entangling process--a linear optics controlled-NOT gate operating with coincident detection--by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.
[show abstract][hide abstract] ABSTRACT: Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.
[show abstract][hide abstract] ABSTRACT: We show that it is possible to perform tomographic characterization of the state of a n-qubit quantum system by performing measurement on a single component only. Implications for quantum information technology will be discussed
[show abstract][hide abstract] ABSTRACT: We experimentally demonstrate an all-optical quantum gate that, with high fidelity, reproduces the entanglement and truth table of a controlled-NOT. We completely characterize it using quantum process tomography, obtaining an average process fidelity of 0.81
[show abstract][hide abstract] ABSTRACT: We investigate a fundamental limitation on the measurement of spatial coherence for highly incoherent fields. We model the near-field detection scheme, required for such a measurement, with pointlike induced dipoles. We find that this fully vector model sets a characteristic length scale beyond which the spatial coherence of an optical field cannot be accurately measured. This length scale forms an uncertainty relationship with the photodetector integration time.
[show abstract][hide abstract] ABSTRACT: We describe a detector for weak optical fields employing an atomic vapor as the active medium, combined with the "cycling transition" readout perfected for ion traps. Theoretical calculations suggest detection efficiency >99% may be attainable.
Quantum Electronics and Laser Science, 2003. QELS. Postconference Digest; 07/2003
[show abstract][hide abstract] ABSTRACT: We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction.
In particular, the possibility of mode–mode coupling, which can be a source of decoherence in trapped ion quantum computation,
or can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible
Applied Physics B 02/2003; 76(3):199-208. · 1.78 Impact Factor
[show abstract][hide abstract] ABSTRACT: Using a scalar dipole model, we find that the fundamental limitation on the measurement of spatial coherence by near-field probes can be understood in terms of a simple scattering model.
[show abstract][hide abstract] ABSTRACT: Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however, to quantify the entanglement of a state in order to quantify the quantum information processing significance of a state. It is known that the fully entangled fraction has a direct relationship to the fidelity of teleportation maximized under the actions of local unitary operations. In the case of two qubits we point out that the fully entangled fraction can also be related to the fidelities, maximized under the actions of local unitary operations, of other important quantum information tasks such as dense coding, entanglement swapping and quantum cryptography in such a way as to provide an inclusive measure of these entanglement applications. For two qubit systems the fully entangled fraction has a simple known closed-form expression and we establish lower and upper bounds of this quantity with the concurrence. This approach is readily extendable to more complicated systems.
[show abstract][hide abstract] ABSTRACT: Summary form only given. Characterizing the entanglement of a general bipartite quantum system is a difficult problem. Most measures involve difficult extremizations and their physical motivation is not always clear. In this paper we propose an experimental measure of entanglement based on a modified version of the familiar teleportation protocol of Bennett et al. (1993). Briefly, teleportation traditionally involves two parties, Alice and Bob. Initially, Alice has a qubit in an unknown quantum state which she would like to communicate to Bob and Bob has two qubits in an entangled Einstein-Podolsky-Rosen (EPR) pair. To accomplish this transfer, Bob shares one qubit of his EPR pair with Alice. She then performs a joint measurement or Bell measurement on her two qubits and relays this information back to Bob over a classical channel. Bob then uses the outcome of Alice's Bell measurement to transform his qubit, with a local unitary transformation, into the original quantum state, always with a fidelity of one.
[show abstract][hide abstract] ABSTRACT: We briefly review the development and theory of an experiment to investigate quantum computation with trapped calcium ions.
The ion trap, laser and ion requirements are determined, and the parameters required for simple quantum logic operations are
[show abstract][hide abstract] ABSTRACT: We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric down-conversion. The states are characterized using measures of entanglement and entropy determined from tomographically determined density matrices. The tangle-entropy plane is introduced as a graphical representation of these states, and the theoretic upper bound for the maximum amount of entanglement possible for a given entropy is presented. Such a combination of general quantum state creation and accurate characterization is an essential prerequisite for quantum device development.
[show abstract][hide abstract] ABSTRACT: Two-qubit states occupy a large and relatively unexplored Hilbert space. Such states can be succinctly characterized by their degree of entanglement and purity. In this letter we investigate entangled mixed states and present a class of states that have the maximum amount of entanglement for a given linear entropy. Comment: 4 pages, 3 figures
[show abstract][hide abstract] ABSTRACT: Summary form only given. Experimental techniques for measurement of the quantum state of light have been the subject of intensive investigation for some time. Tomographic techniques have been applied to experiments such as the homodyne measurement of the Wigner function of a single mode of light and of the density matrix of the polarization degrees of freedom of a pair of entangled photons. In this technique, the density matrix (or Wigner function) which characterizes the quantum state of the system being measured is found from a linear transformation of experimental data. There are a number of drawbacks to the method, principally in that the recovered state might not, because of experimental noise, correspond to a physical state. For example, density matrices for any quantum state must be Hermitian, positive semi-definite matrices with unit trace. The tomographically measured matrices often fail to be positive semi-definite. To avoid this problem, the maximum likelihood approach to the estimation of quantum states has been developed. We evaluate two different approaches to the maximum likelihood technique, namely defining the likelihood function f as a weighted sum of squared variances from measured data, and defining it in terms of information content. These are compared with results of standard tomographical schemes.