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It depends. For a single molecule interacting with one mode of a biphoton probe, we show that the spectroscopic information has three contributions, only one of which is a genuine two-photon contribution. When all the scattered light can be measured, solely this contribution exists and can be fully extracted using unentangled measurements. Furthermore, this two-photon contribution can, in principle, be matched by an optimised but unentangled single-photon probe. When the matter system spontaneously emits into inaccessible modes, an advantage due to entanglement can not be ruled out. In practice, time-frequency entanglement does enhance spectroscopic performance of the oft-studied weakly-pumped spontaneous parametric down conversion (PDC) probes. For two-level systems and coupled dimers, more entangled PDC probes yield more spectroscopic information, even in the presence of emission into inaccessible modes. Moreover, simple, unentangled measurements can capture between 60% - 90% of the spectroscopic information. We thus establish that biphoton spectroscopy using source-engineered PDC probes and unentangled measurements can provide tangible quantum enhancement. Our work underscores the intricate role of entanglement in single-molecule spectroscopy using quantum light., Comment: 18+14 pages, 12+14 figures, 1+0 tables

We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress towards the realisation of programmable hybrid analogue-digital quantum simulators., Comment: 16 pages, 4 figures

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments. This will result in the development of novel quantum sensors and a means to probe the foundations of quantum physics at the interface with gravity. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. These new technologies will open up the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade., Comment: 9 pages, 2 figures, submitted as a Research Campaign Whitepaper for the BPS2023 Decadal Survey

We study the fundamental limits of the precision of estimating parameters of a quantum matter system when it is probed by a travelling pulse of quantum light. In particular, we focus on the estimation of the interaction strength between the pulse and a two-level atom, equivalent to the estimation of the dipole moment. Our analysis of single-photon pulses highlights the interplay between the information gained from the absorption of the photon by the atom as measured in absorption spectroscopy, and the perturbation to the temporal mode of the photon due to spontaneous emission. Beyond the single-photon regime, we introduce an approximate model to study more general states of light in the limit of short pulses, where spontaneous emission can be neglected. We also show that for a vast class of entangled biphoton states, quantum entanglement between the signal mode interacting with the atom and the idler mode provides no fundamental advantage and the same precision can be obtained with a separable state. We conclude by studying the estimation of the electric dipole moment of a sodium atom using quantum light. Our work initiates a quantum information theoretic methodology for developing the theory and practice of quantum light spectroscopy., Comment: v2: 30 pages, 10 figures, Fig. 7 fixes an error in Fig. 8 of v1, appendix E replaces appendix B of v1

We study quantum-limited 3D magnetometry using two qubits. Two qubits form the smallest multi-qubit system for 3D magnetometry, the simultaneous estimation of three phases, as it is impossible with a single qubit. We provide an analytical expression for the Holevo-Cram��r-Rao bound (HCRB),the fundamental attainable quantum bound of multiparameter estimation, for 3D magnetometry using two-qubit pure states and show its attainability by rank-1 projective measurements. We also examine the attainability of the HCRB in the presence of dephasing noise using numerical methods. While attaining the HCRB may require collective measurements over infinitely many copies, we find that for high noise the HCRB is practically saturated by two copies only. In the low noise regime, up to three copies are unable to attain the HCRB. More generally, we introduce new multiparameter channel bounds to compare quantum-classical and classical-quantum strategies where multiple independent copies of the state are entangled before or after recording the parameters respectively. We find that their relative performance depends on the noise strength, with theclassical-quantum strategy performing better for high noise. We end with shallow quantum circuits that approach the fundamental quantum limit set by the HCRB for two-qubit 3D magnetometry using up to three copies., 19 pages, 9 figures

We formulate multiparameter quantum estimation in the parametric and semiparametric setting. While the Holevo Cram��r-Rao bound (CRB) requires no substantial modifications in moving from the former to the latter, we generalize the Helstrom CRB appropriately. We show that the Holevo CRB cannot be greater than twice the generalized Helstrom CRB. We also present a tighter, intermediate, bound. Finally, we show that for parameters encoded in the first moments of a Gaussian state there always exists a Gaussian measurement that gives a classical Fisher information matrix that is one-half of the quantum Fisher information matrix., v2 New coauthor, new and more general results, streamlined presentation. 10 pages, no figures. v3 (same manuscript) Main results have been merged with arXiv:1906.09871 and published on PRX (DOI:10.1103/PhysRevX.10.031023)

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multi-parameter quantum estimation is the Holevo Cram��r-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multi-qubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a non-trivial interplay between the HCRB and incompatibility, and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless two-qubit case., 6+9 pages, 2+2 figures. Comments are welcome

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph's trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of `agents', e.g., income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macroscopic measure of graph centralization. Concretely, we show that the von Neumann index can be used to bound the graph's Theil index, and thus we provide a direct characterization of graph centralization via the von Neumann index. Because of the algebraic similarities between the bound and the Theil index, we call the bound the von Neumann Theil index. %From an information theoretic perspective, the von Neumann Theil index describes the mutual information between the quantum state corresponding to a graph and the maximally mixed state (which corresponds to the complete graph). We elucidate our ideas by providing examples and a discussion of different $n=7$ vertex graphs. We also discuss how the von Neumann Theil index provides a more comprehensive measure of centralization when compared to traditional centralization measures, and when compared to the graph's classical Theil index. This is because it more accurately accounts for macro-structural changes that occur from micro-structural changes in the graph (e.g., the removal of a vertex). Finally, we provide future direction, showing that the von Neumann Theil index can be generalized by considering the R\'enyi entropy. We then show that this generalization can be used to bound the negative logarithm of the graph's Jain fairness index.

While building a universal quantum computer remains challenging, devices of restricted power such as the so-called one pure qubit model have attracted considerable attention. An important step in the construction of these limited quantum computational devices is the understanding of whether the verification of the computation within these models could be also performed in the restricted scheme. Encoding via blindness (a cryptographic protocol for delegated computing) has proven successful for the verification of universal quantum computation with a restricted verifier. In this paper, we present the adaptation of this approach to the one pure qubit model, and present the first feasible scheme for the verification of delegated one pure qubit model of quantum computing., Comment: 31 pages, 3 figures, fixed numbering of theorems

Positivity of quantum discord is shown to be equivalent to the strong sub additivity of the Von-Nuemann entropy. This leads to a connection between the mother protocol of quantum information theory [A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537, (2009)] and quantum discord. We exploit this to show that quantum discord is a measure coherence in the performance of the mother protocol. Since the mother protocol is a unification of an important class of problems (those that are bipartite, unidirectional and memoryless), we show quantum discord to be a measure of coherence in these protocols. Our work generalizes an earlier operational interpretation of quantum discord provided in terms of quantum state merging [V. Madhok and A. Datta, Phys. Rev. A 83, 032323, (2011)]., Comment: To be published in Springer's Lecture Notes in Computer Science as proceedings of The sixth Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC,2011) under the title `Quantum discord in quantum information theory - From strong subadditivity to the Mother protocol'

This paper deals with the entanglement, as quantified by the negativity, of pure quantum states chosen at random from the invariant Haar measure. We show that it is a constant (0.72037) multiple of the maximum possible entanglement. In line with the results based on the concentration of measure, we find evidence that the convergence to the final value is exponentially fast. We compare the analytically calculated mean and standard deviation with those calculated numerically for pure states generated via pseudorandom unitary matrices proposed by Emerson et. al. [Science, 302, 3098, (2003)]. Finally, we draw some novel conclusions about the geometry of quantum states based on our result., Comment: 15 pages, 2 figures

We derive bounds on the entanglement of formation of states of a 4xN bipartite system using two entanglement monotones constructed from operational separability criteria. The bounds are used simultaneously as constraints on the entanglement of formation. One monotone is the negativity, which is based on the Peres positive-partial-transpose criterion. For the other, we formulate a monotone based on a separability criterion introduced by Breuer (H.-P. Breuer, e-print quant-ph/0605036)., Comment: 4 pages, 3 figures

The probable observation of a supersolid helium phase was recently reported by Kim {\it et al}. In this article, we confirm their speculation. Based on a theoretical model for solid helium-4, we show that the emergence of such a phase is inevitable. This is the first instance of Bose-Einstein condensation (BEC) in a solid. We calculate the BEC transition temperature ($T_c$) and the Landau critical velocity ($v_c$) from the model, which respectively are 215 mK and $251 \mu \rm{ms^{-1}}$. They are in excellent agreement with the experimental results; $T_c=$175 mK and $v_c \leq 300 \mu \rm{ms^{-1}}$. We also prove that our model possesses the necessary and sufficient condition for the emergence of supersolidity. We briefly comment about similar behaviour in $^3$He., Comment: 4 pages, 2 figues, Revtex4

We show analytically that the {\it Zitterbewegung} and Klein Paradox, such well known aspects of the Dirac Equation are not found in the case of Bosons. We use the Kemmer-Duffin-Harish Chandra formalism with $\beta$ matrices to arrive at our results, Comment: 5 pages, no figures

The objective of the proposed macroscopic quantum resonators (MAQRO) mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments at the interface with gravity. Developing the necessary technologies, achieving the required sensitivities and providing the necessary isolation of macroscopic quantum systems from their environment will lay the path for developing novel quantum sensors. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. Recent scientific and technological developments since the original proposal of MAQRO promise the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade., Quantum Science and Technology, 8 (1), ISSN:2058-9565

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this letter we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the maximal theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation., 4 pages + appendix, 2 figures

Quantum properties of optical modes are typically assessed by observing their photon statistics or the distribution of their quadratures. Both particle- and wave-like behaviours deliver important information, and each may be used as a resource in quantum-enhanced technologies. Weak-field homodyne detection provides a scheme which combines the wave- and particle-like descriptions. Here we show that it is possible to observe a wave-like property such as the optical coherence across Fock basis states in the detection statistics derived from discrete photon counting. We experimentally demonstrate these correlations using two weak-field homodyne detectors on each mode of two classes of two-mode entangled states. Furthermore, we theoretically describe the response of weak-field homodyne detection on a two-mode squeezed state in the context of generalised Bell inequalities. Our work demonstrates the potential of this technique as a tool for hybrid continuous/discrete-variable protocols on a phenomenon that explicitly combines both approaches., Comment: 19 pages, 12 figures (arXiv version) -- Supplementary Figure 7 modified and minor typos fixed

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase shift and the amplitude of phase diffusion, at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states -- split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental setup for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements., Comment: Published in Nature Communications. Supplementary Information available at http://www.nature.com/ncomms/2014/140404/ncomms4532/extref/ncomms4532-s1.pdf

Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cramer-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters, and has implications for sophisticated sensing scenarios such as quantum imaging., Comment: 9 pages, 6 figures

We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each individual phase separately, as well as improvements over classical strategies. Our strategy provides an advantage in the variance of the estimation over individual quantum estimation schemes that scales as O(d) where d is the number of phases. Finally, we study the attainability of this limit using realistic probes and photon-number-resolving detectors. This is a problem in which an intrinsic advantage is derived from the estimation of multiple parameters simultaneously., Accepted by Physical Review Letters