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The purpose of this article is to provide a novel approach and justification of the idea that classical physics and quantum physics can neither function nor even be conceived one without the other - in line with ideas attributed to e.g. Niels Bohr or Lev Landau. Though this point of view may go against current common wisdom, we will show that it perfectly fits with empirical evidence, and can be maintained without giving up physical realism. In order to place our arguments in a convenient historical perspective, we will proceed as if we were following the path of a police investigation, about the demise, or vanishing, of some valuable properties of the two electrons in the helium atom. We will start from experimentally based evidence in order to analyse and explain physical facts, moving cautiously from a classical to a quantum description, without mixing them up. The overall picture will be that the physical properties of microscopic systems are quantized, as initially shown by Planck and Einstein, and they are also contextual, i.e. that they can be given a physical sense only by embedding a microscopic system within a macroscopic measurement context., Comment: 11 pages, 3 figures. In v2 abstract rewritten and minor edition and clarification in the text

In the foundations of quantum mechanics, the Kolmogorovian Censorship (KC) stipulates that quantum probabilities can be identified with classical, Kolmogorovian probabilities when considering a specified measurement context. Then in any given measurement context it is possible to build a Kolmogorovian probability distribution, or equivalently a hidden variable theory; however this distribution must be matched to the chosen context. In a loophole-free Bell test, the remote random choices of measurements (polarizers orientations) have the purpose to prevent that this matching can be obtained from any relativistically causal transmission between the source and the detectors. Then the matching (required to violate Bell's inequalities) may be obtained either by an instantaneous influence at a distance between the source and the detectors (explicit nonlocality), or by assuming that it is pre-established before the actual experiment takes place (super-determinism). If both influence at a distance and super-determinism are not accepted on physical grounds, a third way is still available, called "predictive incompleteness": it tells that the usual quantum state $\psi$ is incomplete, as long as the measurement context has not been specified. In agreement with the general quantum framework called CSM (Contexts, Systems and Modalities) we argue that predictive incompleteness is the correct quantum way to understand the violation of Bell's inequalities., Comment: 4 pages, no figure

Quantum Key Distribution (QKD) enables secret key exchange between two remote parties with information-theoretic security rooted in the laws of quantum physics. Encoding key information in continuous variables (CV), such as the values of quadrature components of coherent states of light, brings implementations much closer to standard optical communication systems, but this comes at the price of significant complexity in the digital signal processing techniques required for operation at low signal-to-noise ratios. In this work, we wish to lower the barriers to entry for CV-QKD experiments associated to this difficulty by providing a highly modular, open source software that is in principle hardware agnostic and can be used in multiple configurations. We benchmarked this software, called QOSST, using an experimental setup with a locally generated local oscillator, frequency multiplexed pilots and RF-heterodyne detection, and obtained state-of-the-art secret key rates of the order of Mbit/s over metropolitan distances at the asymptotic limit. We hope that QOSST can be used to stimulate further experimental advances in CV-QKD and be improved and extended by the community to achieve high performance in a wide variety of configurations., Comment: 15 pages, 8 figures; Corrected names in metadata and file

Quantum Key Distribution (QKD) is a prominent application in the field of quantum cryptography providing information-theoretic security for secret key exchange. The implementation of QKD systems on photonic integrated circuits (PICs) can reduce the size and cost of such systems and facilitate their deployment in practical infrastructures. To this end, continuous-variable (CV) QKD systems are particularly well-suited as they do not require single-photon detectors, whose integration is presently challenging. Here we present a CV-QKD receiver based on a silicon PIC capable of performing balanced detection. We characterize its performance in a laboratory QKD setup using a frequency multiplexed pilot scheme with specifically designed data processing allowing for high modulation and secret key rates. The obtained excess noise values are compatible with asymptotic secret key rates of 2.4 Mbit/s and 220 kbit/s at an emulated distance of 10 km and 23 km, respectively. These results demonstrate the potential of this technology towards fully integrated devices suitable for high-speed, metropolitan-distance secure communication., Comment: 11 pages, 13 figures; Changed figure 8, acknowledgments updated

We argue that a clear view on quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows a framework in which quantum mechanics can be constructed, in a complete mathematically consistent way. This is made possible by using general operator algebras to extend the mathematical description of the physical world towards macroscopic systems. Such an approach goes beyond the usual type I operator algebras used in standard textbook quantum mechanics. This avoids a major pitfall, which is the temptation to make the usual type I formalism 'universal'. This may also provide a meta-framework for both classical and quantum physics, shedding a new light on ancient conceptual antagonisms, and clarifying the status of quantum objects. Beyond exploring remote corners of quantum physics, we expect these ideas to be helpful to better understand and develop quantum technologies.

Within the framework of quantum contextuality, we discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. We emphasize that whereas Kochen-Specker's is essentially a no-go theorem, Gleason's provides a mathematical justification of Born's rule. Our extracontextual approach requires however a way to describe the ``Heisenberg cut''. Following an article by John von Neumann on infinite tensor products, this can be done by noticing that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorisation. Such an intrinsically contextual approach provides a unified mathematical model including both quantum and classical physics, that appear as required incommensurable facets in the description of nature., Comment: 8 pages, 3 figures. To appear in Journal of Physics: Conference Series as the Proceedings of the DICE 2022 Conference, Castiglioncello, Italy. Section II has overlap with the unpublished preprint arXiv:2201.00371 [quant-ph]

We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradiction arises if one admits that agents must agree on what is considered as a system and what is not. In such a contextually objective approach of quantum mechanics, the apparent contradiction is automatically removed. We also discuss why this mutual agreement between agents is already implicit in the standard formulations of quantum mechanics, and why removing it leads to inconsistencies., Comment: 8 pages, 3 figures

With the Nobel Prize attributed to Aspect, Clauser, and Zeilinger, the international scientific community acknowledged the fundamental importance of the experimental violation of Bell's inequalities. It is however still debated what fails in Bell's hypotheses, leading to these inequalities, and usually summarized as "local realism", or maybe more appropriately "classical local realism". The most common explanation is "quantum non-locality", that remains however fully compatible with relativistic causality; this makes wondering whether any non-local phenomenon is really involved in these experiments. Here we want to recapitulate another option, sometimes called "predictive incompleteness", closely related to the idea that the usual state vector $\psi$ is incomplete indeed, as it was claimed by Einstein, Podolsky and Rosen. However, the right way to complete $\psi$ has nothing to do with hidden variables, but requires to specify the measurement context, as it was claimed by Bohr. Here we will consider the simple case of two spin 1/2, or two qubits, in order to keep the argument simple, but it does apply generally in quantum mechanics., Comment: 2 pages, no figure

A recently published patent (https://www.ipo.gov.uk/p-ipsum/Case/PublicationNumber/GB2590064) has claimed the development of a novel quantum key distribution protocol purporting to achieve long-range quantum security without trusted nodes and without use of quantum repeaters. Here we present a straightforward analysis of this claim, and reach the conclusion that it is largely unfounded., Comment: 9 pages, 2 figures and 1 table

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorization. By interpreting physically this mathematical fact, we show that it provides a natural way to describe the "Heisenberg cut", as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature., Comment: 13 pages, no figure. In v2 some clarifications added

Quantum key distribution (QKD) enables the establishment of secret keys between users connected via a channel vulnerable to eavesdropping, with information-theoretic security, that is, independently of the power of a malevolent party. QKD systems based on the encoding of the key information on continuous variables (CV), such as the values of the quadrature components of coherent states, present the major advantage that they only require standard telecommunication technology. However, the most general security proofs for CV-QKD required until now the use of Gaussian modulation by the transmitter, complicating practical implementations. Here, we experimentally implement a protocol that allows for arbitrary, Gaussian-like, discrete modulations, whose security is based on a theoretical proof that applies very generally to such situations. These modulation formats are compatible with the use of powerful tools of coherent optical telecommunication, allowing our system to reach a performance of tens of megabit per second secret key rates over 25 km., Comment: 6 pages, 6 figures

The purpose of this note is to complete the interesting review on quantum contextuality [1] that appeared recently. In particular we will introduce and discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems, and also to shift the emphasis from the first to the second one. We will also argue that whereas Kochen-Specker's is essentially a negative result (a no-go theorem), Gleason's is a positive one since it provides a mathematical justification of Born's rule. The link between these issues is provided by a specific quantum feature that we call extravalence., Comment: 4 pages, no figure

We designed a CV-QKD system with off-the-shelf components and established the feasibility of distributing 67.6 and 66.8 Mb/s secret key rates on average over a 9.5 km SMF link, using respectively probabilistically shaped 64 and 256 QAM, and relying on a novel analytical security proof., Comment: This work has been presented at the conference ECOC 2021 Bordeaux on the 09/16/2021, and published in the Proceedings of this conference

We demonstrate, for the first time to our knowledge, continuous-variable quantum key distribution using probabilistically-shaped 1024-QAM and true local oscillator, achieving 38.3Mb/s secret key rate over 9.5km, averaged over the transmission time of 100 blocks., Comment: This work has been presented at the conference OFC 2021 San Francisco on the 06/11/2021, and published in the Proceedings of this conference

In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that are accessible to a quantum system, and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason's theorem was emphasized, with the argument that CSM provides a physical justification for Gleason's hypotheses. Here we extend this result by showing that an essential one among these hypotheses - the need of unitary transforms to relate different contexts - can be removed and is better seen as a necessary consequence of Uhlhorn's theorem., Comment: 4 pages, no figure. This article is a continuation of [1] with some overlap for the ease of reading

A Robotic Mobile Fulfillment System is a robotised parts-to-picker system that is particularly well-suited for e-commerce warehousing. One distinguishing feature of this type of warehouse is its high storage modularity. Numerous robots are moving shelves simultaneously, and the shelves can be returned to any open location after the picking operation is completed. This work focuses on the real-time storage allocation problem to minimise the travel time of the robots. An efficient -- but computationally costly -- Monte Carlo Tree Search method is used offline to generate high-quality experience. This experience can be learned by a neural network with a proper coordinates-based features representation. The obtained neural network is used as an action predictor in several new storage policies, either as-is or in rollout and supervised tree search strategies. Resulting performance levels depend on the computing time available at a decision step and are consistently better compared to real-time decision rules from the literature., Comment: 22 pages, 7 figures

In this article we argue that in quantum mechanics, and in opposition to classical physics, it is impossible to say that an isolated quantum system "owns" a physical property. Some properties of the system, its mass for example, belong to it in a sense close to that of classical physics; but most often a property must be attributed to the system within a context. We give simple motivations for adopting this point of view, and show that it clarifies many issues in quantum physics., Comment: This is a preprint of a chapter for the book 'The Quantum-Like Revolution: A Festschrift for Andrei Khrennikov' edited by Arkady Plotnitsky and Emmanuel Haven, Springer 2021. Edited version in v2

E-commerce with major online retailers is changing the way people consume. The goal of increasing delivery speed while remaining cost-effective poses significant new challenges for supply chains as they race to satisfy the growing and fast-changing demand. In this paper, we consider a warehouse with a Robotic Mobile Fulfillment System (RMFS), in which a fleet of robots stores and retrieves shelves of items and brings them to human pickers. To adapt to changing demand, uncertainty, and differentiated service (e.g., prime vs. regular), one can dynamically modify the storage allocation of a shelf. The objective is to define a dynamic storage policy to minimise the average cycle time used by the robots to fulfil requests. We propose formulating this system as a Partially Observable Markov Decision Process, and using a Deep Q-learning agent from Reinforcement Learning, to learn an efficient real-time storage policy that leverages repeated experiences and insightful forecasts using simulations. Additionally, we develop a rollout strategy to enhance our method by leveraging more information available at a given time step. Using simulations to compare our method to traditional storage rules used in the industry showed preliminary results up to 14\% better in terms of travelling times., Comment: 19 pages, 2 tables, 6 figures

It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, that we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing to make contextual inferences, which can in turn explain why quantum non locality does not contradict relativistic causality. But if the usual quantum state $\psi$ is predictively incomplete, how to complete it ? We give here a set of new arguments to show that $\psi$ should be completed indeed, not by looking for any "hidden variables", but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events., Comment: 7 pages, 2 figures. In v2 same text, one Annex added with more arguments and examples. In v3 some precisions and references added. In v4 new abstract, and some clarifications added

This review covers recent theoretical and experimental efforts to extend the application of the continuous-variable quantum technology of light beyond "Gaussian" quantum states, such as coherent and squeezed states, into the domain of "non-Gaussian" states with negative Wigner functions. Starting with basic Gaussian nonclassicality associated with single- and two-mode vacuum states produced by means of parametric down-conversion and applying a set of standard tools, such as linear interferometry, coherent state injection, and conditional homodyne and photon number measurements, one can implement a large variety of optical states and processes that are relevant in fundamental quantum physics as well as quantum optical information processing. We present a systematic review of these methods, paying attention to both fundamental and practical aspects of their implementation, as well as a comprehensive overview of the results achieved therewith.

In standard quantum mechanics (QM), a state vector $| \psi \rangle$ may belong to infinitely many different orthogonal bases, as soon as the dimension $N$ of the Hilbert space is at least three. On the other hand, a complete physical observable $A$ (with no degeneracy left) is associated with a $N$-dimensional orthogonal basis of eigenvectors. In an idealized case, measuring $A$ again and again will give repeatedly the same result, with the same eigenvalue. Let us call this repeatable result a modality $\mu$, and the corresponding eigenstate $| \psi \rangle$. A question is then: does $| \psi \rangle$ give a complete description of $\mu$ ? The answer is obviously no, since $| \psi \rangle$ does not specify the full observable $A$ that allowed us to obtain $\mu$; hence the physical description given by $| \psi \rangle$ is incomplete, as claimed by Einstein, Podolsky and Rosen in their famous article in 1935. Here we want to spell out this provocative statement, and in particular to answer the questions: if $| \psi \rangle$ is an incomplete description of $\mu$, what does it describe ? is it possible to obtain a complete description, maybe algebraic ? Our conclusion is that the incompleteness of standard QM is due to its attempt to describe systems without contexts, whereas both are always required, even if they can be separated outside the measurement periods., Comment: 7 pages, no figure. In v3 first section rewritten in a more pedagogical form, and some additions later on

In previous articles we presented a simple set of axioms named Contexts, Systems and Modalities (CSM), where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain (or rather infer) Born's rule within this framework. Our approach is compared with other former and recent derivations, and its strong links with Gleason's theorem are particularly emphasized., Comment: 6 pages, 3 figures

In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" required to define these modalities. In the present article we provide a unified picture of quantum measurements within our approach, and justify further the role of the system-context dichotomy, and of quantum interferences. We also discuss links with stochastic quantum thermodynamics, and with algebraic quantum theory., Comment: 8 pages, 2 figures, submitted following the Vaxjo 2019 conference "Quantum Information Revolution: Impact to Foundations"

After reminding the main issues at stake in the famous Einstein-Bohr debate initiated in 1935, we tentatively propose a way to get them closer, thus shedding a new light on this historical discussion., Comment: 2 pages, no figure, submitted following the conference "Worlds of Entanglement", Santiago, Chili 2019

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution., Comment: 11 pages, 5 figures; v2: added discussion of more general quadrature amplitude modulation schemes, v3: close to published version

Contrary to the claims made in Ref. [1], the recent Bell tests by Giustina et al. and Shalm et al. do not suffer from a "photon identification loophole". The model discussed in Ref. [1] is exploiting the well-known detection loophole, that is precisely what was closed in the recent experiments., Comment: 2 pages, 1 figure. Code available as an ancillary file

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of "What is quantum in quantum randomness", i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to answer. In a first part, we explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programs inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyze quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness opened in the emerging field of quantum thermodynamics., Comment: This article will appear in Philosophical Transaction A, following the Royal Society Symposium "Foundations of quantum mechanics and their impact on Contemporary Society"

We develop the point of view where Quantum Mechanics results from the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. We point out the specific roles of "extracontextuality" and "extravalence" of modalities, and relate them to the Kochen-Specker and Gleason theorems., Comment: Article prepared as the Proceedings of the conference "Foundations of quantum mechanics and their impact on contemporary society", 11-12 December 2017, The Royal Society, London, UK. In v2 some edition and clarification following referee remarks; to appear in Phil. Trans. R. Soc. A (2018)

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions., Comment: This is an improved version of arXiv:1505.01369 [quant-ph]. In v2 clarifications on the link between axioms and mathematics

Preparing highly entangled quantum states between remote parties is a major challenge for quantum communications [1-8]. Particularly promising in this context are the N00N states, which are entangled N-photon wavepackets delocalized between two different locations, providing measurement sensitivity limited only by the uncertainty principle [1, 10-15]. However, these states are notoriously vulnerable to losses, making it difficult both to share them between remote locations, and to recombine them to exploit interference effects. Here we address this challenge by utilizing the reverse version of the Hong-Ou-Mandel effect [16] to prepare a high-fidelity two-photon N00N state shared between two parties connected by a lossy optical channel. Furthermore, we demonstrate that the enhanced phase sensitivity can be directly exploited in the two distant locations, and we remotely prepare superpositions of coherent states, known as Schr\"odinger's cat states" [17, 18].

We discuss the recently observed "loophole free" violation of Bell's inequalities in the framework of a physically realist view of quantum mechanics, which requires that physical properties are attributed jointly to a system, and to the context in which it is embedded. This approach is clearly different from classical realism, but it does define a meaningful "quantum realism" from a general philosophical point of view. Consistently with Bell test experiments, this quantum realism embeds some form of non-locality, but does not contain any action at a distance, in agreement with quantum mechanics., Comment: This article is closely related to arxiv:1409.2120, with some parts condensed and others expanded, in order to spell out how the present approach explains quantum non-locality. In v2 some clarifications and improvements following referees remarks

We experimentally characterize the optical nonlinear response of a cold atomic medium placed inside an optical cavity, and excited to Rydberg states. The excitation to S and D Rydberg levels is carried out via a two-photon transition in an EIT (electromagnetically induced transparency) configuration, with a weak (red) probe beam on the lower transition, and a strong (blue) coupling beam on the upper transition. The observed optical nonlinearities induced by S states for the probe beam can be explained using a semi-classical model with van der Waals' interactions. For the D states, it appears necessary to take into account a dynamical decay of Rydberg excitations into a long-lived dark state. We show that the measured nonlinearities can be explained by using a Rydberg bubble model with a dynamical decay., Comment: 8 pages, 6 figures

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

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual quantum formalism, within a new conceptual framework that is discussed heuristically in details. The structure of Quantum Mechanics, from its probabilistic nature to its mathematical expression, appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities., Comment: 6 pages, no figure

In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose to modify the quantum ontology, by requiring that physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary., Comment: 9 pages, 3 figures. In v2 extended section VI on EPR, and new section VII on measurements

The employ of a noiseless linear amplifier (NLA) has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a NLA has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suitable for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of this effective system, and illustrate its potential by applying it to loss compensation and reduction of phase uncertainty., Comment: 8 pages, 3 figures

We experimentally demonstrate that a non-classical state prepared in an atomic memory can be efficiently transferred to a single mode of free-propagating light. By retrieving on demand a single excitation from a cold atomic gas, we realize an efficient source of single photons prepared in a pure, fully controlled quantum state. We characterize this source using two detection methods, one based on photon-counting analysis, and the second using homodyne tomography to reconstruct the density matrix and Wigner function of the state. The latter technique allows us to completely determine the mode of the retrieved photon in its fine phase and amplitude details, and demonstrate its nonclassical field statistics by observing a negative Wigner function. We measure a photon retrieval efficiency up to 82% and an atomic memory coherence time of 900 ns. This setup is very well suited to study interactions between atomic excitations, and to use them in order to create and manipulate more sophisticated quantum states of light with a high degree of experimental control., Comment: 5 pages, 5 figures

We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be exactly evaluated in a steady state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple "universal scaling" formula to determine the dispersive optical nonlinearity of the medium. We also develop a novel technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that only involve two-body correlations, which can be solved numerically. All average populations and coherences are then obtained straightforwardly., Comment: 9 pages, 4 figures

Distributing secret keys with information-theoretic security is arguably one of the most important achievements of the field of quantum information processing and communications. The rapid progress in this field has enabled quantum key distribution (QKD) in real-world conditions and commercial devices are now readily available. QKD systems based on continuous variables present the major advantage that they only require standard telecommunication technology, and in particular, that they do not use photon counters. However, these systems were considered up till now unsuitable for long-distance communication. Here, we overcome all previous limitations and demonstrate for the first time continuous-variable quantum key distribution over 80 km of optical fibre. The demonstration includes all aspects of a practical scenario, with real-time generation of secret keys, stable operation in a regular environment, and use of finite-size data blocks for secret information computation and key distillation. Our results correspond to an implementation guaranteeing the strongest level of security for QKD reported to date for such long distances and pave the way to practical applications of secure quantum communications.

We observe and measure dispersive optical non-linearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical non-linearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.