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Quantum illumination uses quantum correlations to enhance the detection of an object in the presence of background noise. This advantage has been shown to exist even if one uses non-optimal direct measurements on the two correlated modes. Here we present a protocol that mimics the behaviour of quantum illumination, but does not use correlated or entangled modes. Instead, the protocol uses coherent (or phase-randomized coherent) pulses with randomly chosen intensities. The intensities are drawn from a distribution such that the average state looks thermal. Under appropriate conditions, the mimic protocol can perform similarly to quantum illumination schemes that use direct measurements. This holds even for a reflectance as low as $10^{-7}$. We also present an analytic condition which allows one to determine the sets of parameters in which each protocol works best., Comment: 13 pages, 9 figures

Global-scale quantum communication networks will require efficient long-distance distribution of quantum signals. Optical fibre communication channels have range constraints due to exponential losses in the absence of quantum memories and repeaters. Satellites enable intercontinental quantum communication by exploiting more benign inverse square free-space attenuation and long sight lines. However, the design and engineering of satellite quantum key distribution (QKD) systems are difficult and characteristic differences to terrestrial QKD networks and operations pose additional challenges. The typical approach to modelling satellite QKD (SatQKD) has been to estimate performances with a fully optimised protocol parameter space and with few payload and platform resource limitations. Here, we analyse how practical constraints affect the performance of SatQKD for the Bennett-Brassard 1984 (BB84) weak coherent pulse decoy state protocol with finite key size effects. We consider engineering limitations and trade-offs in mission design including limited in-orbit tunability, quantum random number generation rates and storage, and source intensity uncertainty. We quantify practical SatQKD performance limits to determine the long-term key generation capacity and provide important performance benchmarks to support the design of upcoming missions., Comment: 15 pages, 11 figures, and 1 table. Updated discussions and final accepted version

Quantum key distribution (QKD) is a theoretically proven future-proof secure encryption method that inherits its security from fundamental physical principles. Craft Prospect, working with a number of UK organisations, has been focused on miniaturising the technologies that enable QKD so that they may be used in smaller platforms including nanosatellites. The significant reduction of size, and therefore the cost of launching quantum communication technologies either on a dedicated platform or hosted as part of a larger optical communications will improve potential access to quantum encryption on a relatively quick timescale. The ROKS mission seeks to be among the first to send a QKD payload on a CubeSat into low Earth orbit, demonstrating the capabilities of newly developed modular quantum technologies. The ROKS payload comprises a quantum source module that supplies photons randomly in any of four linear polarisation states fed from a quantum random number generator; an acquisition, pointing, and tracking system to fine-tune alignment of the quantum source beam with an optical ground station; an imager that will detect cloud cover autonomously; and an onboard computer that controls and monitors the other modules, which manages the payload and assures the overall performance and security of the system. Each of these modules have been developed with low SWaP for CubeSats, but with interoperability in mind for other satellite form factors. We present each of the listed components, together with the initial test results from our test bench and the performance of our protoflight models prior to initial integration with the 6U CubeSat platform systems. The completed ROKS payload will be ready for flight at the end of 2022, with various modular components already being baselined for flight and integrated into third party communication missions., Comment: 13 pages with 25 figures. Presented at Small Satellite Conference: https://digitalcommons.usu.edu/smallsat/2022/all2022/163/. Any comments are welcome

Terrestrial free-space quantum key distribution is ideally suited for deployment in dense urban environments. The transition from laboratory to commercial deployment, however, raises a number of important engineering and deployment issues. Here, we investigate these issues for efficient BB84 using a weak coherent pulse-decoy state protocol. We calculate expected key lengths for different environmental conditions and when the scope for optimisation of protocol parameters is restricted due to practical considerations. In particular, we find that for a fixed receiver basis choice probability, it can be advantageous to allow the transmitter to have a different basis choice probability depending on varying channel loss and background light levels. Finally, we examine the effects of pulse intensity uncertainty finding that they can dramatically reduce the key length. These results can be used to determine the loss budget for the free-space optics of a QKD systems and assist in their design., Comment: 24 pages and 10 figures

In satellite-based quantum key distribution (QKD), the number of secret bits that can be generated in a single satellite pass over the ground station is severely restricted by the pass duration and the free-space optical channel loss. High channel loss may decrease the signal-to-noise ratio due to background noise, reduce the number of generated raw key bits, and increase the quantum bit error rate (QBER), all of which have detrimental effects on the output secret key length. Under finite-size security analysis, higher QBER increases the minimum raw key length necessary for non-zero secret key length extraction due to less efficient reconciliation and post-processing overheads. We show that recent developments in finite key analysis allow three different small-satellite-based QKD projects CQT-Sat, UK-QUARC-ROKS, and QEYSSat to produce secret keys even under very high loss conditions, improving on estimates based on previous finite key bounds. This suggests that satellites in low Earth orbit can satisfy finite-size security requirements, but remains challenging for satellites further from Earth. We analyse the performance of each mission to provide an informed route toward improving the performance of small-satellite QKD missions. We highlight the short and long-term perspectives on the challenges and potential future developments in small-satellite-based QKD and quantum networks. In particular, we discuss some of the experimental and theoretical bottlenecks, and improvements necessary to achieve QKD and wider quantum networking capabilities in daylight and at different altitudes., Comment: 15 pages, 8 figures, and 5 tables. Improved analysis with detailed discussions and perspectives. Comments welcome

Documentation for version 1.1 of the open-source software SatQuMA: Satellite Quantum Modelling & Analysis., Comment: https://github.com/cnqo-qcomms/SatQuMA

Concerted efforts are underway to establish an infrastructure for a global quantum internet to realise a spectrum of quantum technologies. This will enable more precise sensors, secure communications, and faster data processing. Quantum communications are a front-runner with quantum networks already implemented in several metropolitan areas. A number of recent proposals have modelled the use of space segments to overcome range limitations of purely terrestrial networks. Rapid progress in the design of quantum devices have enabled their deployment in space for in-orbit demonstrations. We review developments in this emerging area of space-based quantum technologies and provide a roadmap of key milestones towards a complete, global quantum networked landscape. Small satellites hold increasing promise to provide a cost effective coverage required to realised the quantum internet. We review the state of art in small satellite missions and collate the most current in-field demonstrations of quantum cryptography. We summarise important challenges in space quantum technologies that must be overcome and recent efforts to mitigate their effects. A perspective on future developments that would improve the performance of space quantum communications is included. We conclude with a discussion on fundamental physics experiments that could take advantage of a global, space-based quantum network., Comment: 26 pages, 9 figures. Comments welcome. This paper is a preprint of a paper submitted to IET Quantum Communication. If accepted, the copy of record will be available at the IET Digital Library

Global quantum communications will enable long-distance secure data transfer, networked distributed quantum information processing, and other entanglement-enabled technologies. Satellite quantum communication overcomes optical fibre range limitations, with the first realisations of satellite quantum key distribution (SatQKD) being rapidly developed. However, limited transmission times between satellite and ground station severely constrains the amount of secret key due to finite-block size effects. Here, we analyse these effects and the implications for system design and operation, utilising published results from the Micius satellite to construct an empirically-derived channel and system model for a trusted-node downlink employing efficient BB84 weak coherent pulse decoy states with optimised parameters. We quantify practical SatQKD performance limits and examine the effects of link efficiency, background light, source quality, and overpass geometries to estimate long-term key generation capacity. Our results may guide design and analysis of future missions, and establish performance benchmarks for both sources and detectors., Comment: 15 pages, 8+4 figures, 2 tables. Version 2 includes additional results

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of non-boson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space., Comment: Close to the version published in PRA

Quantum correlations between two systems can be impaired by the presence of an environment, as it can make systems decohere. We wish to evaluate how much coherence has been irreversibly lost. To do so, we study two qubits which leak correlations into an arbitrarily large environment and we find that our ability to steer one of them to the most coherent set of states possible by acting on the other is given by the sub-fidelity of two conditional states of the environment. Sub-fidelity is a quantity that was already known, but that until now lacked an operational interpretation. Furthermore, we conjecture the existence of a family of measures, of which fidelity and sub-fidelity are the first two, which measure the irreversibility of decoherence as we gain access to more and more degrees of freedom of the enviroment.

We determine the shared information that can be extracted from time-bin entangled photons using frame encoding. We consider photons generated by a general down-conversion source and also model losses, dark counts and the effects of multiple photons within each frame. Furthermore, we describe a procedure for including other imperfections such as after-pulsing, detector dead-times and jitter. The results are illustrated by deriving analytic expressions for the maximum information that can be extracted from high-dimensional time-bin entangled photons generated by a spontaneous parametric down conversion. A key finding is that under realistic conditions and using standard SPAD detectors one can still choose frame size so as to extract over 10 bits per photon. These results are thus useful for experiments on high-dimensional quantum-key distribution system., Comment: 18 pages, 6 figures

When quantum systems interact with the environment they lose their quantum properties, such as coherence. Quantum erasure makes it possible to restore coherence in a system by measuring its environment, but accessing the whole of it may be prohibitive: realistically one might have to concentrate only on an accessible subspace and neglect the rest. If that is the case, how good is quantum erasure? In this work we compute the largest coherence $\langle \mathcal C\rangle$ that we can expect to recover in a qubit, as a function of the dimension of the accessible and of the inaccessible subspaces of its environment. We then imagine the following game: we are given a uniformly random pure state of $n+1$ qubits and we are asked to compute the largest coherence that we can retrieve on one of them by optimally measuring a certain number $0\leq a\leq n$ of the others. We find a surprising effect around the value $a\approx n/2$: the recoverable coherence sharply transitions between 0 and 1, indicating that in order to restore full coherence on a qubit we need access to only half of its physical environment (or in terms of degrees of freedom to just the square root of them). Moreover, we find that the recoverable coherence becomes a typical property of the whole ensemble as $n$ grows., Comment: 4 pages, 5 figures

In practical applications of quantum information science, quantum systems can have non-negligible interactions with the environment, and this generally degrades the power of quantum protocols as it introduces noise. Counteracting this by appropriately measuring the environment (and therefore projecting its state) would require access all the necessary degrees of freedom, which in practice can be far too hard to achieve. To better understand one's limitations, we calculate the upper bound of optimal quantum erasure (i.e. the highest recoverable visibility, or "coherence"), when erasure is realistically limited to an accessible subspace of the whole environment. In the particular case of a two-dimensional accessible environment, the bound is given by the sub-fidelity of two particular states of the \emph{inaccessible} environment, which opens a new window into understanding the connection between correlated systems. We also provide an analytical solution for a three-dimensional accessible environment. This result provides also an interesting operational interpretation of sub-fidelity. We end with a statistical analysis of the expected visibility of an optimally erased random state and we find that 1) if one picks a random pure state of 2 qubits, there is an optimal measurement that allows one to distill a 1-qubit state with almost 90\% visibility and 2) if one picks a random pure state of 2 qubits in an inaccessible environment, there is an optimal measurement that allows one to distill a 1-qubit state with almost twice its initial visibility., Comment: 7 pages, 6 figures

The task of measuring in two mutually unbiased bases is central to many quantum information protocols, as well as being of fundamental interest. Increasingly, there is an experimental focus on generating and controlling high-dimensional photonic states. One approach is to use the arrival time of a photon, which can be split into discrete time bins. An important problem associated with such states is the difficulty in experimentally realizing a measurement that is mutually unbiased with respect to the time-of-arrival. We propose a simple and compact scheme to measure in both the time of arrival basis and a basis that is approximately mutually unbiased with respect to the arrival time., Comment: Accepted in EPL, 4.1 pages and 2 figures

Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy-time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy-time entanglement based QKD. This observations leads us to investigate the security of modified Franson-based-protocols, where Alice and Bob have two or more Franson interferometers. We show that such setups can improve the sensitivity against attacks that localize the photons to multiple temporal locations. While our results do not constituting a full security proof, they do show that a single pair of Franson interferometers is not secure and that multiple such interferometers could be a promising candidate for experimentally realizable high-dimensional QKD., Comment: 14 pages (single column format)

A key goal of quantum communication is to determine the maximum number of bits shared between two quantum systems. An important example of this is in entanglement based quantum key distribution (QKD) schemes. A realistic treatment of this general communication problem must take account of the nonideal nature of the entanglement source and the detectors. The aim of this paper is to give such a treatment. We obtain analytic expression for the mutual information in terms of experimental parameters. The results are applied to communication schemes that rely on spontaneous parametric down conversion to generate entangled photons. We show that our results can be applied to tasks such as calculating the optimal rate of bits per photon in high dimensional time bin encoded QKD protocols (prior to privacy amplification). A key finding for such protocols is that by using realistic experimental parameters, one can obtain over 10 bits per photon. We also show how our results can be applied to characterize the capacity of a fibre array and to quantify entanglement using mutual information., Comment: 9 pages, 5 figures, accepted for publication in Phys Rev A

We derive an analytical form of the Schmidt modes of spontaneous parametric down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We show that these correspond to Hermite-Gauss (HG) or Laguerre-Gauss (LG) modes only for a specific value of their width, and we show how such value depends on the experimental parameters. The Schmidt modes that we explicitly derive allow one to set up an optimised projection basis that maximises the mutual information gained from a joint measurement. The possibility of doing so with LG modes makes it possible to take advantage of the properties of orbital angular momentum eigenmodes. We derive a general entropic entanglement measure using the R\'enyi entropy as a function of the Schmidt number, K, and then retrieve the von Neumann entropy, S. Using the relation between S and K we show that, for highly entangled states, a non-ideal measurement basis does not degrade the number of shared bits by a large extent. More specifically, given a non-ideal measurement which corresponds to the loss of a fraction of the total number of modes, we can quantify the experimental parameters needed to generate an entangled SPDC state with a sufficiently high dimensionality to retain any given fraction of shared bits., Comment: 8 pages, 3 figures

We investigate the entanglement produced by a multi-path interferometer that is composed of two symmetric multiports, with phase shifts applied to the output of the first multiport. Particular attention is paid to the case when we have a single photon entering the interferometer. For this situation we derive a simple condition that characterize the types of entanglement that one can generate. We then show how one can use the results from the single photon case to determine what kinds of multi-photon entangled states one can prepare using the interferometer., Comment: 6 pages, 2 figures, accepted for publication in European Journal of Physics D

We investigate multi-boson interference. A Hamiltonian is presented that treats pairs of bosons as a single composite boson. This Hamiltonian allows two pairs of bosons to interact as if they were two single composite bosons. We show that this leads to the composite bosons exhibiting novel interference effects such as Hong-Ou-Mandel interference. We then investigate generalizations of the formalism to the case of interference between two general composite bosons. Finally, we show how one can realize interference between composite bosons in the two atom Dicke model.

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons., Comment: Accepted for publication in Journal of Modern Optics

We investigate the uncertainty associated with a joint quantum measurement of two components of spin of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the marginal entropies, and obtain lower bounds for each of these quantities. For the case of joint measurements where we measure each spin observable equally well, these lower bounds are tight., Comment: 13 pages, introduction re-written and extended discussion of results

We examine the problem of estimating the expectation values of two observables when we have a finite number of copies of an unknown qubit state. Specifically we examine whether it is better to measure each of the observables separately on different copies or to perform a joint measurement of the observables on each copy. We find that joint measurements can sometimes provide an advantage over separate measurements, but only if we make estimates of an observable based solely on the results of measurements of that observable. If we instead use both sets of results to estimate each observable then we find that individual measurements will be better. Finally we consider estimating the expectation values of three complementary observables for an unknown qubit., Comment: 11 pages, 3 figures, submitted to PRA

The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it corresponds to making measurements diagonal in a corresponding Schmidt basis. More generally, it is shown that the maximum correlation may be characterised in terms of a `correlation basis' for the joint density operator, which defines the corresponding (nondegenerate) optimal measurements. The maximum coincidence rate for spin measurements on two-qubit systems is determined to be (1+s)/2, where s is the spectral norm of the spin correlation matrix, and upper bounds are obtained for n-valued measurements on general bipartite systems. It is shown that the maximum coincidence rate is never greater than the computable cross norm measure of entanglement, and a much tighter upper bound is conjectured. Connections with optimal state discrimination and entanglement bounds are briefly discussed., Comment: Revtex, no figures

A joint measurement of two observables is a {\it simultaneous} measurement of both quantities upon the {\it same} quantum system. When two quantum-mechanical observables do not commute, then a joint measurement of these observables cannot be accomplished by projective measurements alone. In this paper we shall discuss the use of quantum cloning to perform a joint measurement of two components of spin associated with a qubit system. We introduce a cloning scheme which is optimal with respect to this task. This cloning scheme may be thought to work by cloning two components of spin onto its outputs. We compare the proposed cloning machine to existing cloners., Comment: 7 pages, 2 figures, submitted to PRA