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Since the 1970's it has been known that black hole (and other) horizons are truly thermodynamic in nature. More generally, surfaces which are not horizons have also been conjectured to behave thermodynamically. Initially, for surfaces microscopically expanded from a horizon to so-called stretched horizons, and more recently, for more general ordinary surfaces in the emergent gravity program. To test these conjectures we ask whether such surfaces satisfy an analogue to the first law of thermodynamics (as do horizons). For static asymptotically-flat spacetimes we find that such a first law holds on horizons. We rigorously prove that this law remains an excellent approximation for stretched horizons, but perhaps counter-intuitively this result illustrates the insufficiency of the laws of black hole mechanics alone from implying truly thermodynamic behavior. For surfaces away from horizons in the emergent gravity program the first law fails (with the exception of fully spherically symmetric scenarios) thus undermining the key thermodynamic assumption of this program., 12 pages, 2 figures, Published in Nature Communications

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension $d=2$. Indeed, relying on conventional Hilbert-space representations entails an exponential overhead with increasing dimension. Some general upper and lower bounds for various success measures, such as (entanglement) fidelity, are known, but some become trivial in higher dimensions. Here we construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called "pretty-good measurements" with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension $d$ and low number of ports $N$, obtaining in addition a simple upper bound. The results for low $N$ and arbitrary $d$ show that the fidelity asymptotically approaches ${N}/{d^2}$ for large $d$, confirming the performance of one lower bound from the literature., Comment: 7 pages, Published in Scientific Reports

We show that the apparent horizon and the region near $r=0$ of an evaporating charged, rotating black hole are timelike. It then follows that for black holes in nature, which invariably have some rotation, have a channel, via which classical or quantum information can escape to the outside, while the black hole shrinks in size. We discuss implications for the information loss problem., Minor typos corrected, version to match the published version in the International Journal of Modern Physics D

We consider a quantum relay which is used by two parties to perform several continuous-variable protocols of quantum communication, from entanglement distribution (swapping and distillation), to quantum teleportation, and quantum key distribution. The theory of these protocols is suitably extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise in the bosonic environment. In the worst case scenario where bipartite entanglement is completely lost at the relay, we show that the various protocols can be reactivated by the assistance of classical (separable) correlations in the environment. In fact, above a critical amount, these correlations are able to guarantee the distribution of a weaker form of entanglement (quadripartite), which can be localized by the relay into a stronger form (bipartite) that is exploitable by the parties. Our findings are confirmed by a proof-of-principle experiment where we show, for the first time, that memory effects in the environment can drastically enhance the performance of a quantum relay, well beyond the single-repeater bound for quantum and private communications., Main text plus Supplemental Material. 30 pages. 23 figures. Expands arXiv:1505.07457 and includes new results

A general security proof of continuous variable (CV) measurement device independent (MDI) quantum key distribution (QKD) should not be automatically reduced to the analysis of one-mode Gaussian attacks (in particular, independent entangling-cloner attacks). To stress this point, the present work provides a very simple (almost trivial) argument, showing that there are an infinite number of two-mode Gaussian attacks that cannot be reduced to or simulated by one-mode Gaussian attacks. This result further confirms that the security analysis of CV-MDI-QKD must generally involve a careful minimization over two-mode attacks as originally performed in (Pirandola et al, 2015 Nature Photon. 9, 397–402; arXiv:1312.4104 (2013)).

Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements., Quantum Communications and Quantum Imaging XVI, SPIE Optical Engineering + Applications, 19 - 23 August 2018, San Diego CA, United States

We consider quantum discrimination of bosonic loss based on both symmetric and asymmetric hypothesis testing. In both approaches, an entangled resource is able to outperform any classical strategy based on coherent-state transmitters in the regime of low photon numbers. In the symmetric case, we then consider the low energy detection of bacterial growth in culture media. Assuming an exponential growth law for the bacterial concentration and the Beer-Lambert law for the optical transmissivity of the sample, we find that the use of entanglement allows one to achieve a much faster detection of growth with respect to the use of coherent states. This performance is also studied by assuming an exponential photo-degradable model, where the concentration is reduced by increasing the number of photons irradiated over the sample. This investigation is then extended to the readout of classical information from suitably-designed photo-degradable optical memories., REVTeX. 14 pages. 11 figures

The prevalent view that evaporating black holes should simply be smaller black holes has been challenged by the firewall paradox. In particular, this paradox suggests that something different occurs once a black hole has evaporated to one-half its original surface area. Here, we derive variations of the firewall paradox by tracking the thermodynamic entropy within a black hole across its entire lifetime and extend it even to anti-de Sitter space–times. Our approach sweeps away many unnecessary assumptions, allowing us to demonstrate a paradox exists even after its initial onset (when conventional assumptions render earlier analyses invalid). The most natural resolution may be to accept firewalls as a real phenomenon. Further, the vast entropy accumulated implies a deep firewall that goes ‘all the way down’ in contrast with earlier work describing only a structure at the horizon. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels, we may express the quantum Cram\'er Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit., Comment: Short review paper. REVTeX 10 pages. 6 figures

We consider the Braunstein-Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various forms of convergence are then discussed within adaptive protocols, where the simulation error must be propagated to the output of the protocol by means of a "peeling" argument, following techniques from PLOB [arXiv:1510.08863]. Finally, as an application of the peeling argument and the various topologies of convergence, we provide complete rigorous proofs for recently-claimed strong converse bounds for private communication over Gaussian channels., Accepted version. Establishes a general criterion for the uniform convergence of teleportation simulation for an arbitrary Gaussian channel. Clarifying the use of the Braunstein-Kimble teleportation protocol, it also provides complete proofs for the claims presented in WTB arXiv:1602.08898, beyond the first rigorous proof already given in arXiv:1711.09909

Advances in quantum communication will come from investment in hybrid technologies, explain Stefano Pirandola and Samuel L. Braunstein.

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of several fundamental channels, including the bosonic lossy channel. We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein-Kimble teleportation protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution., Comment: Review paper which also contains new results. Published version. REVTeX. 28 pages. 2 tables and 4 figures

Reply to 'Discrete and continuous variables for measurement-device-independent quantum cryptography'

We study the quantum version of a decision tree classifier to fill the gap between quantum computation and machine learning. The quantum entropy impurity criterion which is used to determine which node should be split is presented in the paper. By using the quantum fidelity measure between two quantum states, we cluster the training data into subclasses so that the quantum decision tree can manipulate quantum states. We also propose algorithms constructing the quantum decision tree and searching for a target class over the tree for a new quantum object.

We consider the secret key capacity of the thermal loss channel, which is modeled by a beam splitter mixing an input signal mode with an environmental thermal mode. This capacity is the maximum value of secret bits that two remote parties can generate by means of the most general adaptive protocols assisted by unlimited and two-way classical communication. To date, only upper and lower bounds are known. The present work improves the lower bound by resorting to Gaussian protocols based on suitable trusted-noise detectors., 10 pages, 2 figures

CEVIRI Orijinal Adi: International journal of parallel, emergent and distributed systems Yazarlar: Susan Stepney Samuel L. Braunstein John A. Clark Andy Tyrrell Andrew Adamatzky Robert E. Smith Tom Addis Colin Johnson Jonathan Timmis Peter Welch Robin Milner Derek Partridge

We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources., Main text (4 pages) plus Appendices

As one of the applications of Grover search, an exact quantum algorithm for the symmetric weight decision problem of a Boolean function has been proposed recently. Although the proposed method shows a quadratic speedup over the classical approach, it only applies to the symmetric case of a Boolean function whose weight is one of the pair {0 < w 1 < w 2 < 1, w 1 + w 2 = 1}. In this article, we generalize this algorithm in two ways. Firstly, we propose a quantum algorithm for the more general asymmetric case where {0 < w 1 < w 2 < 1}. This algorithm is exact and computationally optimal. Secondly, we build on this to exactly solve the multiple weight decision problem for a Boolean function whose weight as one of {0 < w 1 < w 2 < · · · < w m < 1}. This extended algorithm continues to show a quantum advantage over classical methods. Thirdly, we compare the proposed algorithm with the quantum counting method. For the case with two weights, the proposed algorithm shows slightly lower complexity. For the multiple weight case, the two approaches show different performance depending on the number of weights and the number of solutions. For smaller number of weights and larger number of solutions, the weight decision algorithm can show better performance than the quantum counting method. Finally, we discuss the relationship between the weight decision problem and the quantum state discrimination problem.

As with any viable technology, quantum-information processors have to deal with imperfections. The experimental implementation of a quantum-error correction code indicates how imperfections can be handled in a system where quantum information is encoded in continuous variables. Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. To protect fragile quantum-superposition states from corruption through so-called decoherence noise, some form of error correction is needed. Therefore, the discovery of quantum error correction1,2 (QEC) was a key step to turn the field of quantum information from an academic curiosity into a developing technology. Here, we present an experimental implementation of a QEC code for quantum information encoded in continuous variables, based on entanglement among nine optical beams3. This nine-wave-packet adaptation of Shor’s original nine-qubit scheme1 enables, at least in principle, full quantum error correction against an arbitrary single-beam error.

We consider the continuous-variable protocol of Pirandola et al. [Nature Photonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strategies against the quantum links explicitly showing that, at fixed transmissivity and thermal noise, two-mode coherent attacks are optimal, manifestly outperforming one-mode collective attacks based on independent entangling cloners. Such an advantage is shown both in terms of security threshold and secret-key rate., 10 pages, 8 figures, up-to-date reference, close to published version

Quantum cryptography achieves a formidable task—the remote distribution of secret keys by exploiting the fundamental laws of physics. Quantum cryptography is now headed towards solving the practical problem of constructing scalable and secure quantum networks. A significant step in this direction has been the introduction of measurement-device independence, where the secret key between two parties is established by the measurement of an untrusted relay. Unfortunately, although qubit-implemented protocols can reach long distances, their key rates are typically very low, unsuitable for the demands of a metropolitan network. Here we show, theoretically and experimentally, that a solution can come from the use of continuous-variable systems. We design a coherent-state network protocol able to achieve remarkably high key rates at metropolitan distances, in fact three orders of magnitude higher than those currently achieved. Our protocol could be employed to build high-rate quantum networks where devices securely connect to nearby access points or proxy servers. An end-to-end continuous-variable quantum key distribution system with an untrusted node is proposed. A proof-of-principle experiment shows that 10−1 secret key bits per relay use are distributed at 4 dB loss, corresponding to 20 km in optical fibre.

Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations., Comment: Nature Photonics Review. Comments are welcome. This is a slightly-expanded arXiv version (14 pages, 5 figure, 1 table)

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be used as subroutines for larger algorithms their success rate is important. We propose a partial search algorithm which achieves success with unit probability.

This Letter reports results from time domain measurements in a terahertz pulsed imaging system and suggests that a mechanical resetting mechanism in the pump-probe delay stage results in a small but resolvable noise signal. In the setup described here, this effect dominates all other sources of noise such as the background Johnson noise or shot noise, and can hence be isolated and analysed in detail. An analysis of the noise signal is used to estimate the physical limitations of the pump-probe system being employed. A comparison of the results with an analytic prediction allows us to formulate a useful and general signature of registration noise, that should make it easy to detect in any sufficiently narrowband signal.

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.

Høyer has given a generalisation of the Deutsch–Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes between functions which are either perfectly balanced (m-to-one) or constant, with certainty, and using a single quantum query. Here, we show that this algorithm (which we call the Deutsch–Jozsa–Høyer algorithm) can in fact deal with a broader range of promises, which we define in terms of the irreducible representations of G.

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field., Comment: accepted for publication in Reviews of Modern Physics

A time-dependent dielectric cmedium is used to model a time-varying beam-splitter inside a cavity. The time-varying boundary conditions smoothly evolve from a highly transmitting to a highly reflecting beam-splitter. These approximately correspond to a transformation from a single cavity to a pair of cavities. Quantum field-theoretic calculations show that such a smooth change yields non-singular evolution of the field. However, it predicts a production of photons up to frequencies comparable to the rate of change of the transition. We find that a time-varying beam-splitter operating at optical frequencies would produce an observable number of photons.

1. The challengeA gateway event [35] is a change to a system that leads to the possibility of huge increases inkinds and levels of complexity. It opens up a whole new kind of phase space to the system’sdynamics.Gatewayeventsduringevolutionoflifeonearthincludetheappearanceofeukaryotes(organisms with a cell nucleus), an oxygen atmosphere, multi-cellular organisms and grass.Gatewayeventsduringthedevelopmentofmathematicsincludeeachinventionofanewclassofnumbers (negative, irrational, imaginary, ...), and dropping Euclid’s parallel postulate.A gateway event produces a profound and fundamental change to the system: Oncethrough the gateway, life is never the same again. We are currently poised on the threshold ofa significant gateway event in computation: That of breaking free from many of our current“classical computational” assumptions. Our Grand Challenge for computer science isto journey through the gateway event obtained by breaking our current classicalcomputational assumptions, and thereby develop a mature science of Non-ClassicalComputation2. Journeys versus goals

We present a simple numerical optimization procedure to search for highly entangled states of 2, 3, 4 and 5 qubits. We develop a computationally tractable entanglement measure based on the negative partial transpose criterion, which can be applied to quantum systems of an arbitrary number of qubits. The search algorithm attempts to optimize this entanglement cost function to find the maximal entanglement in a quantum system. We present highly entangled 4-qubit and 5-qubit states discovered by this search. We show that the 4-qubit state is not quite as entangled, according to two separate measures, as the conjectured maximally entangled Higuchi–Sudbery state. Using this measure, these states are more highly entangled than the 4-qubit and 5-qubit GHZ states. We also present a conjecture about the NPT measure, inspired by some of our numerical results, that the single-qubit reduced states of maximally entangled states are all totally mixed.

It has recently been argued that the inability to measure the absolute phase of an electromagnetic field prohibits the representation of a laser's output as a quantum optical coherent state. This argument has generally been considered technically correct but conceptually disturbing. Indeed, it would seem to place in question the very concept of the coherent state. Here we show that this argument fails to take into account a fundamental principle that not only re-admits the coherent state as legitimate, but formalizes a fundamental concept about model building in general, and in quantum mechanics in particular., This work has been submitted to Physics Letters A and presented in the meeting of JPS in 2002

We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyperresolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of principle of quantum lithography, and we address the question of state preparation and the fabrication of suitable photoresists., Comment: 8 pages, to appear in Journal of Optics B

We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable., Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue)

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is provided by the quantum Hoeffding bound. After a brief review of these notions, we show how this bound can be simplified for pure states. We then provide a general recipe for its computation in the case of multimode Gaussian states, also showing its connection with other easier-to-compute lower bounds. In particular, we provide analytical formulas and numerical results for important classes of one- and two-mode Gaussian states., REVTeX. Published version

We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.

A transformation achieving the optimal symmetric N-to-M cloning of coherent states is presented. Its implementation only requires a phase-insensitive linear amplifier and a network of beam splitters. An experimental demonstration of this continuous-variable cloner should therefore be in the scope of current technology. The link between optimal quantum cloning and optimal amplification of quantum states is also pointed out., Comment: 4 pages, 2 figures

Classical, interferometric, optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result surpasses the usual classical diffraction limit by a factor of N. Since the number of features that can be etched on a two-dimensional surface scales inversely as the square of the feature size, this allows one to write a factor of N^2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric downconversion. It is shown how to write arbitrary 2D patterns by using this method., 9 pages, 2 figures

Quantum teleportation of optical coherent states was demonstrated experimentally using squeezed-state entanglement. The quantum nature of the achieved teleportation was verified by the experimentally determined fidelity F exp = 0.58 ± 0.02, which describes the match between input and output states. A fidelity greater than 0.5 is not possible for coherent states without the use of entanglement. This is the first realization of unconditional quantum teleportation where every state entering the device is actually teleported.

Using a surprising result for the Wronskian of solutions with a common factor we show that all of the linearly independent solutions of linear-homogeneous ODEs have a simple form in a generalized phase-integral representation. This allows the generalization of WKB-like expansions to higher-order differential equations in a way that extends the usual phase-integral methods. This work clarifies the internal structure of phase-integral representations as being discrete transforms over the quasiphases of the linearly independent ODE solutions and hence clarifies the structure of solutions to linear ODEs.

We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of continuous variable codes is robust against imprecision in the error syndromes. A potential implemetation of the scheme is presented., latex with revtex, 4 pages, 3 figures