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Peter van Loock

Publications and source records attributed to Peter van Loock.

At least 127 records · Page 7Linked to original sources

Universal linear Bogoliubov transformations through one-way quantum computation

We show explicitly how to realize an arbitrary linear unitary Bogoliubov transformation (LUBO) on a multi-mode quantum state through homodyne-based one-way quantum computation. Any LUBO can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBOs. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO. Arbitrary input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.

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Demonstration of a universal one-way quantum quadratic phase gate

We demonstrate a quadratic phase gate for one-way quantum computation in the continuous-variable regime. This canonical gate, together with phase-space displacements and Fourier rotations, completes the set of universal gates for realizing any single-mode Gaussian transformation such as arbitrary squeezing. As opposed to previous implementations of measurement-based squeezers, the current gate is fully controlled by the local oscillator phase of the homodyne detector. Verifying this controllability, we give an experimental demonstration of the principles of one-way quantum computation over continuous variables. Moreover, we can observe sub-shot-noise quadrature variances in the output states, confirming that nonclassical states are created through cluster computation.

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Quantum Computing with Continuous-Variable Clusters

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

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Quantum error correction beyond qubits

Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by so-called decoherence noise. Indeed, the discovery of quantum error correction (QEC) turned the field of quantum information from an academic curiosity into a developing technology. Here we present a continuous-variable experimental implementation of a QEC code, based upon entanglement among 9 optical beams. In principle, this 9-wavepacket adaptation of Shor's original 9-qubit scheme allows for full quantum error correction against an arbitrary single-beam (single-party) error.

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A note on quantum error correction with continuous variables

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.

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Quantum control of noisy channels

Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski isomorphism, we express the control of a noisy channel in terms of control of (non-normalized) states, and show how the available resources enter the analysis. Our formalism provides a general scheme for the protection of quantum state transmission when a single use of the physical channel is considered. Moreover, it paves the way to the application of control theoretical tools to the study of noisy channels. We define the notion of complexity of a noisy channel, as a measure of how demanding is to engineer specific manipulations of a channel. We provide some examples of both deterministic and probabilistic protocols leading to a decreased complexity.

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Anyonic statistics with continuous variables

We describe a continuous-variable scheme for simulating the Kitaev lattice model and for detecting statistics of abelian anyons. The corresponding quantum optical implementation is solely based upon Gaussian resource states and Gaussian operations, hence allowing for a highly efficient creation, manipulation, and detection of anyons. This approach extends our understanding of the control and application of anyons and it leads to the possibility for experimental proof-of-principle demonstrations of anyonic statistics using continuous-variable systems.

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Demonstration of a quantum nondemolition sum gate

The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light fields. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U.L. Andersen [\pra {\bf 71}, 042308 (2005)], solely based on offline squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying the criteria for QND measurements in both conjugate quadratures.

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Quantum Repeaters using Coherent-State Communication

We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.

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Experimental generation of four-mode continuous-variable cluster states

Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.

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Continuous-Variable Telecloning with Phase-Conjugate Inputs

We propose a scheme for continuous-variable telecloning with phase-conjugate inputs (PCI). Two cases of PCI telecloning are considered. The first case is where PCI telecloning produces $M$ clones nonlocally and $M$ anticlones locally, or vice versa. This kind of PCI telecloning requires only one EPR (Einstein-Podolsky-Rosen) entangled, two-mode squeezed state as a resource for building the appropriate multi-mode, multipartite entangled state via linear optics. The other case is a PCI telecloning protocol in which both clones and anticlones are created nonlocally. Such a scheme requires two EPR entangled states for the generation of a suitable multipartite entangled state. As our schemes are reversible, optimal cloning fidelities are achieved in the limit of infinite squeezing.

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Practical effects in the preparation of cluster states using weak non-linearities

We discuss experimental effects in the implementation of a recent scheme for performing bus mediated entangling operations between qubits. Here a bus mode, a strong coherent state, successively undergoes weak Kerr-type non-linear interactions with qubits. A quadrature measurement on the bus then projects the qubits into an entangled state. This approach has the benefit that entangling gates are non-destructive, may be performed non-locally, and there is no need for efficient single photon detection. In this paper we examine practical issues affecting its experimental implementation. In particular, we analyze the effects of post-selection errors, qubit loss, bus loss, mismatched coupling rates and mode-mismatch. We derive error models for these effects and relate them to realistic fault-tolerant thresholds, providing insight into realistic experimental requirements.

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Sequential Quantum Teleportation of Optical Coherent States

We demonstrate a sequence of two quantum teleportations of optical coherent states, combining two high-fidelity teleporters for continuous variables. In our experiment, the individual teleportation fidelities are evaluated as F_1 = 0.70 \pm 0.02 and F_2 = 0.75 \pm 0.02, while the fidelity between the input and the sequentially teleported states is determined as F^{(2)} = 0.57 \pm 0.02. This still exceeds the optimal fidelity of one half for classical teleportation of arbitrary coherent states and almost attains the value of the first (unsequential) quantum teleportation experiment with optical coherent states.

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Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light

We describe a system for long-distance distribution of quantum entanglement, in which coherent light with large average photon number interacts dispersively with single, far-detuned atoms or semiconductor impurities in optical cavities. Entanglement is heralded by homodyne detection using a second bright light pulse for phase reference. The use of bright pulses leads to a high success probability for the generation of entanglement, at the cost of a lower initial fidelity. This fidelity may be boosted by entanglement purification techniques, implemented with the same physical resources. The need for more purification steps is well compensated for by the increased probability of success when compared to heralded entanglement schemes using single photons or weak coherent pulses with realistic detectors. The principle cause of the lower initial fidelity is fiber loss; however, spontaneous decay and cavity losses during the dispersive atom/cavity interactions can also impair performance. We show that these effects may be minimized for emitter-cavity systems in the weak-coupling regime as long as the resonant Purcell factor is larger than one, the cavity is over-coupled, and the optical pulses are sufficiently long. We support this claim with numerical, semiclassical calculations using parameters for three realistic systems: optically bright donor-bound impurities such as 19-F:ZnSe with a moderate-Q microcavity, the optically dim 31-P:Si system with a high-Q microcavity, and trapped ions in large but very high-Q cavities.

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Building Gaussian Cluster States by Linear Optics

The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. We show that for any Gaussian cluster state, the canonical generation scheme in terms of QND-type interactions, can be entirely replaced by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful and we propose a systematic way to create cheaper states. As an application, we consider Gaussian cluster computation in multiple-rail encoding. This encoding may reduce errors due to finite squeezing, even when the extra rails are achieved through off-line squeezing and linear optics.

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Examples of Gaussian cluster computation

We give simple examples that illustrate the principles of one-way quantum computation using Gaussian continuous-variable cluster states. In these examples, we only consider single-mode evolutions, realizable via linear clusters. In particular, we focus on Gaussian single-mode transformations performed through the cluster state. Our examples highlight the differences between cluster-based schemes and protocols in which special quantum states are prepared off-line and then used as a resource for the on-line computation.

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Simple criteria for projective measurements with linear optics

We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain easily No-Go theorems for the exact distinguishability of orthogonal quantum states with linear optics including the use of auxiliary photons and conditional dynamics.

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Implementing Non-Projective Measurements via Linear Optics: an Approach Based on Optimal Quantum State Discrimination

We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states.

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