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Blind quantum computing (BQC) is a promising application of distributed quantum systems, where a client can perform computations on a remote server without revealing any details of the applied circuit. While the most promising realizations of quantum computers are based on various matter qubit platforms, implementing BQC on matter qubits remains an outstanding challenge. Using silicon-vacancy (SiV) centers in nanophotonic diamond cavities with an efficient optical interface, we experimentally demonstrate a universal quantum gate set consisting of single- and two-qubit blind gates over a distributed two-node network. Using these ingredients, we perform a distributed algorithm with blind operations across our two-node network, paving the way towards blind quantum computation with matter qubits in distributed, modular architectures., Comment: 47 pages, 29 figures

Neutral atom quantum processors are a promising platform for large-scale quantum computing. Integrating them with an optical cavity enables fast nondestructive qubit readout and access to fast remote entanglement generation for quantum networking. Here, we introduce a platform for coupling single atoms in optical tweezers to a Fabry-Perot Fiber Cavity. Leveraging the strong atom-cavity coupling, we demonstrate fast qubit state readout with 99.960$^{+14}_{-24}\%$ fidelity and two methods for cavity-mediated entanglement generation with integrated error detection. First, we use cavity-carving to generate a Bell state with 91(4)$\%$ fidelity and a 32(1)$\%$ success rate. Second, we perform a cavity-mediated gate with a deterministic entanglement fidelity of 52.5(18)$\%$, increased to 76(2)$\%$ with error detection. The new capabilities enabled by this platform pave the way towards modular quantum computing and networking.

Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and rate of entanglement generation. However, the optimal architectures and entanglement generation schemes are not yet established. Focusing on modular quantum computers with solid-state quantum hardware, we investigate a distributed surface code's error-correcting threshold and logical failure rate. We consider both emission-based and scattering-based entanglement generation schemes for the measurement of non-local stabilizers. Through quantum optical modeling, we link the performance of the quantum error correction code to the parameters of the underlying physical hardware and identify the necessary parameter regime for fault-tolerant modular quantum computation. In addition, we compare modular architectures with one or two data qubits per module. We find that the performance of the code depends significantly on the choice of entanglement generation scheme, while the two modular architectures have similar error-correcting thresholds. For some schemes, thresholds nearing the thresholds of non-distributed implementations ($\sim0.4 \%$) appear feasible with future parameters., Comment: 34 pages, 29 figures

Quantum technologies present new opportunities for fundamental tests of nature. One potential application is to probe the interplay between quantum physics and general relativity - a field of physics with no empirical evidence yet. Here we show that quantum networks open a new window to test this interface. We demonstrate how photon mediated entanglement between atomic or atom-like systems can be used to probe time-dilation induced entanglement and interference modulation. Key are non-local measurements between clocks in a gravitational field, which can be achieved either through direct photon interference or by using auxiliary entanglement. The resulting observable depends on the interference between different proper times, and can only be explained if both quantum theory and general relativity are taken into account. The proposed protocol enables clock interferometry on km-scale separations and beyond. Our work thus shows a realistic experimental route for a first test of quantum theory on curved space-time, opening up new scientific opportunities for quantum networks., Comment: 11 pages, 3 figures, 2 Appendices

The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities > 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware., Comment: 13 pages, 5 figures

Reliable quantum communication over hundreds of kilometers is a daunting yet necessary requirement for a quantum internet. To overcome photon loss, the deployment of quantum repeater stations between distant network nodes is necessary. A plethora of different quantum hardware is being developed for this purpose, each platform with its own opportunities and challenges. Here, we propose to combine two promising hardware platforms in a hybrid quantum repeater architecture to lower the cost and boost the performance of long-distance quantum communication. We outline how ensemble-based quantum memories combined with single-spin photon transducers, which can transfer quantum information between a photon and a single spin, can facilitate massive multiplexing, efficient photon generation, and quantum logic for amplifying communication rates. As a specific example, we describe how a single Rubidium (Rb) atom coupled to nanophotonic resonators can function as a high-rate, telecom-visible entangled photon source with the visible photon being compatible with storage in a Thulium-doped crystal memory (Tm-memory) and the telecom photon being compatible with low loss fiber propagation. We experimentally verify that Tm and Rb transitions are in resonance with each other. Our analysis shows that by employing up to 9 repeater stations, each equipped with two Tm-memories capable of holding up to 625 storage modes, along with four single Rb atoms, one can reach a quantum communication rate of about 10 secret bits per second across distances of up to 1000 km., Comment: 16 pages, 7 figures in total, with 5 appendix sections

Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to investigate the effect of noise and imperfections and to assess their practical value. Here, we implement a variational algorithm designed for optimized parameter estimation on a continuous variable platform based on squeezed light, a key component for high-precision optical phase estimation. We investigate the ability of the algorithm to identify the optimal metrology process, including the optimization of the probe state and measurement strategy for small-angle optical phase sensing. Two different optimization strategies are employed, the first being a gradient descent optimizer using Gaussian parameter shift rules to estimate the gradient of the cost function directly from the measurements. The second strategy involves a gradient-free Bayesian optimizer, fine-tuning the system using the same cost function and trained on the data acquired through the gradient-dependent algorithm. We find that both algorithms can steer the experiment towards the optimal metrology process. However, they find minima not predicted by our theoretical model, demonstrating the strength of variational algorithms in modelling complex noise environments, a non-trivial task., Comment: Main document: 7 pages, 3 figures, Supplementary Material: 14 page, 10 figures

Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pairs, which can significantly reduce the required coherence time of the qubit registers. However, current schemes require fast optical switching, which is experimentally challenging. In addition, the higher degree of error correlation between the generated entangled pairs in qudit protocols compared to qubit protocols has not been studied in detail. We propose a qudit-mediated entangling protocol that completely circumvents the need for optical switches, making it more accessible for current experimental systems. Furthermore, we quantify the amount of error correlation between the simultaneously generated entangled pairs and analyze the effect on entanglement purification algorithms and teleportation-based quantum error correction. We find that optimized purification schemes can efficiently correct the correlated errors, while the quantum error correction codes studied here perform worse than for uncorrelated error models.

Color-centers integrated with nanophotonic devices have emerged as a compelling platform for quantum science and technology. Here we integrate tin-vacancy centers in a diamond waveguide and investigate the interaction with light at the single-photon level. We observe single-emitter induced extinction of the transmitted light up to 25% and measure the nonlinear effect on the photon statistics. Furthermore, we demonstrate fully tunable interference between the reflected single-photon field and laser light back-scattered at the fiber end and show the corresponding controlled change between bunched and anti-bunched photon statistics in the reflected field.

Generating entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote entanglement generation have been proposed, of which many have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimal resource overhead by interspersing repeater nodes that each specializes in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication., Comment: 25 pages, 16 figures, 4 tables

The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of single-qubit Pauli matrices, which can readily be measured with single qubit rotations. The accumulation of shot noise in this approach, however, severely limits the achievable variance for a finite number of measurements. We introduce a novel method, dubbed Coherent Pauli Summation (CPS) that circumvents this limitation by exploiting access to a single-qubit quantum memory in which measurement information can be stored and accumulated. Our algorithm offers a reduction in the required number of measurements for a given variance that scales linearly with the number of Pauli strings of the decomposed observable. Our work demonstrates how a single long-coherence qubit memory can assist the operation of noisy many-qubit quantum devices in a cardinal task., Comment: 2 figures

Generating multiple entangled qubit pairs between distributed nodes is a prerequisite for a future quantum internet. To achieve a practicable generation rate, standard protocols based on photonic qubits require multiple long-term quantum memories, which remains a significant experimental challenge. In this paper, we propose a novel protocol based on $2^m$-dimensional time-bin photonic qudits that allow for the simultaneous generation of multiple ($m$) entangled pairs between two distributed qubit registers and outline a specific implementation of the protocol based on cavity-mediated spin-photon interactions. By adopting the qudit protocol, the required qubit memory time is independent of the transmission loss between the nodes in contrast to standard qubit approaches. As such, our protocol can significantly boost the performance of near-term quantum networks., Comment: 13 pages, 7 figures, accepted by PRX Quantum

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we develop a shadow tomography method for quantum channels that is of independent interest. This protocol can be used to parallelize to learn the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices., Comment: 37 pages, 4 figures. Corrected gap in the proof of previous classical shadow process tomography protocols, included dissipation in the numerics, and improved presentation

Ensuring security and integrity of elections constitutes an important challenge with wide-ranging societal implications. Classically, security guarantees can be ensured based on computational complexity, which may be challenged by quantum computers. We show that the use of quantum networks can enable information-theoretic security for the desirable aspects of a distributed voting scheme in a resource-efficient manner. In our approach, ballot information is encoded in quantum states that enable an exponential reduction in communication complexity compared to classical communication. In addition, we provide an efficient and secure anonymous queuing protocol. As a result, our scheme only requires modest quantum memories with size scaling logarithmically with the number of voters. This intrinsic efficiency together with certain noise-robustness of our protocol paves the way for its physical implementation in realistic quantum networks., Comment: 11 + 15 pages, 4 + 1 figures

As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multi-qubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique characterizes and accounts for state-preparation and measurement (SPAM) errors and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.

With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum algorithms feasible on such devices address a challenge central to the field of quantum metrology: The identification of near-optimal probes and measurement operators for noisy multi-parameter estimation problems. We first introduce a general framework which allows for sequential updates of variational parameters to improve probe states and measurements and is widely applicable to both discrete and continuous-variable settings. We then demonstrate the practical functioning of the approach through numerical simulations, showcasing how tailored probes and measurements improve over standard methods in the noisy regime. Along the way, we prove the validity of a general parameter-shift rule for noisy evolutions, expected to be of general interest in variational quantum algorithms. In our approach, we advocate the mindset of quantum-aided design, exploiting quantum technology to learn close to optimal, experimentally feasible quantum metrology protocols., Comment: 15 pages, 4 figures, many circuits

The realization of a long-distance, distributed quantum network based on quantum memory nodes that are linked by photonic channels remains an outstanding challenge. We propose a quantum network node based on neutral alkali atoms coupled to nanophotonic crystal cavities that combines a long-lived memory qubit with a photonic interface at the telecom range, thereby enabling the long-distance distribution of entanglement over low loss optical fibers. We present a novel protocol for the generation of an atom-photon entangled state which uses telecom transitions between excited states of the alkali atoms. We analyze the realistic implementation of this protocol using rubidium and cesium atoms taking into account the full atomic level structure and properties of the nanophotonic crystal cavity. We find that a high fidelity entangled state can be generated with current technologies, Comment: 16 pages, 6 figures

We describe a resource-efficient approach to studying many-body quantum states on noisy, intermediate-scale quantum devices. We employ a sequential generation model that allows us to bound the range of correlations in the resulting many-body quantum states. From this, we characterize situations where the estimation of local observables does not require the preparation of the entire state. Instead smaller patches of the state can be generated from which the observables can be estimated. This can potentially reduce circuit size and number of qubits for the computation of physical properties of the states. Moreover, we show that the effect of noise decreases along the computation. Our results apply to a broad class of widely studied tensor network states and can be directly applied to near-term implementations of variational quantum algorithms., Comment: 20 pages, 5 figures, 1 Table. Close to published version

We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree-cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations. As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates. We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility. We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations., Comment: Merged article and supplemental material, corrected typos in Eq. (8)-(10) in supplemental material

Networking plays a ubiquitous role in quantum technology. It is an integral part of quantum communication and has significant potential for upscaling quantum computer technologies that are otherwise not scalable. Recently, it was realized that sensing of multiple spatially distributed parameters may also benefit from an entangled quantum network. Here we experimentally demonstrate how sensing of an averaged phase shift among four distributed nodes benefits from an entangled quantum network. Using a four-mode entangled continuous variable (CV) state, we demonstrate deterministic quantum phase sensing with a precision beyond what is attainable with separable probes. The techniques behind this result can have direct applications in a number of primitives ranging from biological imaging to quantum networks of atomic clocks.

We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact through the guided modes of the photonic crystal, and a uniform magnetic field gives rise to large topological band gaps and an almost completely flat topological band. Topological edge states arise on the boundaries of the system that are protected by the large gap against missing lattice sites and to the inhomogeneous broadening of emitters. These results pave the way for exploring topological many-body states in quantum optical systems., Comment: 5 pages, 5 figures + 8 pages, 6 figures SM; see also companion paper arXiv:1810.12815

Quantum networks provide a platform for astronomical interferometers capable of imaging faint stellar objects. In a recent work [arXiv:1809.01659], we presented a protocol that circumvents transmission losses with efficient use of quantum resources and modest quantum memories. Here we analyze a number of extensions to that scheme. We show that it can be operated as a truly broadband interferometer and generalized to multiple sites in the array. We also analyze how imaging based on the quantum Fourier transform provides improved signal-to-noise ratio compared to classical processing. Finally, we discuss physical realizations including photon-detection-based quantum state transfer., Comment: 10 pages, 8 figures; v2 - clarifications and references; v3 - close to published version

We propose a method for optical interferometry in telescope arrays assisted by quantum networks. In our approach, the quantum state of incoming photons along with an arrival time index is stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglement-assisted parity checks at the expected photon arrival rate allows for direct extraction of the phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme (based on efficient quantum data compression) offers an exponential decrease in required entanglement bandwidth. Experimental implementation is then feasible with near-term technology, enabling optical imaging of astronomical objects akin to well-established radio interferometers and pushing resolution beyond what is practically achievable classically., Comment: 7 + 6 pages, 3 + 1 figures; v2 - clarifications and further discussion of implementation; v3 - close to published version

We propose a method for quantum enhanced phase estimation based on continuous variable (CV) quantum teleportation. The phase shift probed by a coherent state can be enhanced by repeatedly teleporting the state back to interact with the phase shift again using a supply of two-mode squeezed vacuum states. In this way, both super resolution and super sensitivity can be obtained due to the coherent addition of the phase shift. The protocol enables Heisenberg limited sensitivity and super- resolution given sufficiently strong squeezing. The proposed method could be implemented with current or near-term technology of CV teleportation., Comment: 5 pagers, 3 figures

Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as e.g. multi-mode entangled states. Our proof is based on a new fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.

Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation and long-lived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including long-range interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such long-range interactions for arbitrary two-dimensional atomic lattices. As applications of our method, we investigate the topological properties of atomic lattices both in free-space and near plasmonic surfaces., Comment: 15 pages, 7 figures

The strong light-matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown in [Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence from spontaneous emission and cavity decay, we find roughly the same level of squeezing for the two schemes scaling as (NC)^(1/2) where C is the single atom cooperativity and N is the total number of atoms. When compared to an ideal squeezing operation, we find that for specific initial states, a dissipative version of the one-axis scheme attains higher fidelity than the unitary one-axis scheme or the two-axis scheme. However, the unitary one-axis and two-axis schemes perform better for general initial states., Comment: 13 pages, 6 figures

We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with non-trivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogues of interacting topological systems., Comment: 11 pages and 9 figures; paper updated to match published version

A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from linear optical quantum computation in order to perform high fidelity quantum gates across a quantum network. The error-detecting properties of the heralded operations ensure high fidelity while the encoding makes it possible to correct for failed attempts such that deterministic and high-quality gates can be achieved. Importantly, this is robust to photon loss, which is typically the main obstacle to photonic based quantum information processing. Overall this approach opens a novel path towards quantum networks with atomic nodes and photonic links., Comment: 5 pages, 4 figures

We propose a method to induce strong effective interactions between photons mediated by an atomic ensemble. To achieve this, we use the so-called stationary light effect to enhance the interaction. Regardless of the single-atom coupling to light, the interaction strength between the photons can be enhanced by increasing the total number of atoms. For sufficiently many atoms, the setup can be viable as a controlled-phase gate for photons. We derive analytical expressions for the fidelities for two modes of gate operation: deterministic and heralded conditioned on the presence of two photons at the output., Comment: 5 pages, 3 figures + Supplemental Material

Efficient interfaces between photons and quantum emitters form the basis for quantum networks and enable nonlinear optical devices operating at the single-photon level. We demonstrate an integrated platform for scalable quantum nanophotonics based on silicon-vacancy (SiV) color centers coupled to nanoscale diamond devices. By placing SiV centers inside diamond photonic crystal cavities, we realize a quantum-optical switch controlled by a single color center. We control the switch using SiV metastable orbital states and verify optical switching at the single-photon level by using photon correlation measurements. We use Raman transitions to realize a single-photon source with a tunable frequency and bandwidth in a diamond waveguide. Finally, we create entanglement between two SiV centers by detecting indistinguishable Raman photons emitted into a single waveguide. Entanglement is verified using a novel superradiant feature observed in photon correlation measurements, paving the way for the realization of quantum networks., Comment: 15 pages and 5 figures. Supplementary Material, 36 pages and 10 figures, available as an ancillary file

We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalise the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the non-classicality test with classical tomography methods based on the inverse Radon transform, which can also be used to establish the quantum nature of a physical system. In particular, we consider a non-classicality test based on the so-called filtered back-projection formula. We show that the general non-classicality test is conceptually simpler, requires less assumptions on the system and is statistically more reliable than the tests based on the filtered back-projection formula. As a specific example, we derive the optimal test for a quadrature squeezed single photon state and show that the efficiency of the test does not change with the degree of squeezing.

We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles., Comment: main manuscript 5 pages with 11 pages of supplementary information

Individual atoms in optical cavities can provide an efficient interface between stationary qubits and flying qubits (photons), which is an essentiel building block for quantum communication. Furthermore, cavity assisted controlled-not (CNOT) gates can be used for swapping entanglement to long distances in a quantum repeater setup. Nonetheless, dissipation introduced by the cavity during the CNOT may increase the experimental difficulty in obtaining long-distance entanglement distribution using these systems. We analyse and compare a number of cavity-based repeater schemes combining various entanglement generation schemes and cavity assisted CNOT gates. We find that a scheme, where high-fidelity entanglement is first generated in a two-photon detection scheme and then swapped to long distances using a recently proposed heralded CZ-gate exhibits superior performance compared to the other schemes. The heralded gate moves the effect of dissipation from the fidelity to the success probability of the gate thereby enabling high-fidelity entanglement swapping. As a result, high-rate entanglement distribution can be achieved over long distances even for low cooperativities of the atom-cavity systems. This high-fidelity repeater is shown to outperform the other cavity-based schemes by up to two orders of magnitude in the rate for realistic parameters and large distances (1000 km)., Comment: 15 pages, 13 figures

Atomic clocks are typically operated by locking a local oscillator (LO) to a single atomic ensemble. In this article we propose a scheme where the LO is locked to several atomic ensembles instead of one. This results in an exponential improvement compared to the conventional method and provides a stability of the clock scaling as $(\alpha N)^{-m/2}$ with $N$ being the number of atoms in each of the $m$ ensembles and $\alpha$ is a constant depending on the protocol being used to lock the LO, Comment: 10 pages, 8 figures

The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near Heisenberg limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence., Comment: 13 pages, 9 figures. Note that new reference: Y. Matsuzaki, S. C. Benjamin, and J. Fitzsimons, Phys. Rev. A 84, 012103 (2011) is added