The size of quantum superpositions as measured with "classical" detectors

We propose a criterion which defines whether a superposition of two photonic components is macroscopic. It is based on the ability to discriminate these components with a particular class of "classical" detectors, namely a photon number measurement with a resolution coarse-grained by noise. We show how our criterion can be extended to a measure of the size of macroscopic superpositions by quantifying the amount of noise that can be tolerated and taking the distinctness of two Fock states differing by N photons as a reference. After applying our measure to several well-known examples, we demonstrate that the superpositions which meet our criterion are very sensitive to phase fluctuations. This suggests that quantifying the macroscopicity of a superposition state through the distinguishability of its components with "classical" detectors is not only a natural measure but also explains why it is difficult to observe superpositions at the macroscopic scale.Comment: 5 pages, 3 figures, updated versio

Proposal for Implementing Device-Independent Quantum Key Distribution based on a Heralded Qubit Amplification

In device-independent quantum key distribution (DIQKD), the violation of a Bell inequality is exploited to establish a shared key that is secure independently of the internal workings of the QKD devices. An experimental implementation of DIQKD, however, is still awaited, since hitherto all optical Bell tests are subject to the detection loophole, making the protocol unsecured. In particular, photon losses in the quantum channel represent a fundamental limitation for DIQKD. Here, we introduce a heralded qubit amplifier based on single-photon sources and linear optics that provides a realistic solution to overcome the problem of channel losses in Bell tests.Comment: 5 pages, 4 figures, 6 page appendi

How difficult it is to prove the quantumness of macroscropic states?

General wisdom tells us that if two quantum states are ``macroscopically distinguishable'' then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum nature of a superposition of two states that can be distinguished without microscopic accuracy. First, we quantify the distinguishability of any given pair of quantum states with measurement devices lacking microscopic accuracy, i.e. measurements suffering from limited resolution or limited sensitivity. Next, we quantify the required stability that have to be fulfilled by any measurement setup able to distinguish their superposition from a mere mixture. Finally, by establishing a relationship between the stability requirement and the ``macroscopic distinguishability'' of the two superposed states, we demonstrate that indeed, the more distinguishable the states are, the more demanding are the stability requirements.Comment: 6 pages, 2 figure

Macroscopic optomechanics from displaced single-photon entanglement

Displaced single-photon entanglement is a simple form of optical entanglement, obtained by sending a photon on a beamsplitter and subsequently applying a displacement operation. We show that it can generate, through a momentum transfer in the pulsed regime, an optomechanical entangled state involving macroscopically distinct mechanical components, even if the optomechanical system operates in the single-photon weak coupling regime. We discuss the experimental feasibility of this approach and show that it might open up a way for testing unconventional decoherence models.Comment: 10 pages, 4 figures, submission coordinated with Gohbadi et al. who reported on similar result

Purification of single-photon entanglement with linear optics

We show that single-photon entangled states of the form |0>|1>+|1>|0> can be purified with a simple linear-optics based protocol, which is eminently feasible with current technology. Besides its conceptual interest, this result is relevant for attractive quantum repeater protocols.Comment: 4 pages, 3 figure

Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.Comment: 9 pages, 4 figures (Accepted for publication in Phys. Rev. A

Quantum Repeaters based on Single Trapped Ions

We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on two-ion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows that the distribution rate of entanglement achievable with such an ion-based quantum repeater protocol is higher by orders of magnitude than the rates that are achievable with the best known schemes based on atomic ensemble memories and linear optics. The main reason is that for trapped ions the entanglement swapping operations are performed deterministically, in contrast to success probabilities below 50 percent per swapping with linear optics. The scheme requires efficient collection of the emitted photons, which can be achieved with cavities, and efficient conversion of their wavelength, which can be done via stimulated parametric down-conversion. We also suggest how to realize temporal multiplexing, which offers additional significant speed-ups in entanglement distribution, with trapped ions

Heralded single phonon preparation, storage and readout in cavity optomechanics

We analyze theoretically how to use the radiation pressure coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state), and release on-demand the stored excitation as a single photon. Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband leads to dynamical backaction amplification and to the creation of correlated photon-phonon pairs. The detection of one Stokes photon thus projects the macroscopic oscillator into a single-phonon Fock state. The non-classical nature of this mechanical state can be demonstrated by applying a readout laser on the lower sideband (i.e. optical cooling) to map the phononic state to a photonic mode, and by performing an autocorrelation measurement on the anti-Stokes photons. We discuss the relevance of our proposal for the future of cavity optomechanics as an enabling quantum technology.Comment: Accepted for publication in Physical Review Letters. Added References 42,4