## Publications

222 results found

Aqua Z, Kim MS, Dayan B, 2019, Generation of optical Fock and W states with single-atom-based bright quantum scissors, *Photonics Research*, Vol: 7, Pages: A45-A45, ISSN: 2327-9125

We introduce a multi-step protocol for optical quantum state engineering that performs as “bright quantum scissors,” namely truncating an arbitrary input quantum state to have at least a certain number of photons. The protocol exploits single-photon pulses and is based on the effect of single-photon Raman interaction, which is implemented with a single three-level Λ system (e.g., a single atom) Purcell-enhanced by a single-sided cavity. A single step of the protocol realizes the inverse of the bosonic annihilation operator. Multiple iterations of the protocol can be used to deterministically generate a chain of single photons in a W state. Alternatively, upon appropriate heralding, the protocol can be used to generate Fock-state optical pulses. This protocol could serve as a useful and versatile building block for the generation of advanced optical quantum states that are vital for quantum communication, distributed quantum information processing, and all-optical quantum computing.

Paige A, Yadin B, Kim M, 2019, Quantum correlations for anonymous metrology, *Quantum*, Vol: 3, Pages: 1-14, ISSN: 2521-327X

We introduce the task of anonymous metrology, in which a physical parameter of an object may be determined without revealing the object's location. Alice and Bob share a correlated quantum state, with which one of them probes the object. Upon receipt of the quantum state, Charlie is then able to estimate the parameter without knowing who possesses the object. We show that quantum correlations are resources for this task when Alice and Bob do not trust the devices in their labs. The anonymous metrology protocol moreover distinguishes different kinds of quantum correlations according to the level of desired security: discord is needed when the source of states is trustworthy, otherwise entanglement is necessary.

Kwon H, Kim M, 2019, Fluctuation theorems for a quantum channel, *Physical Review X*, Vol: 9, ISSN: 2160-3308

We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary non-equilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement.

Milz S, Kim MS, Pollock FA,
et al., 2019, Completely positive divisibility does not mean markovianity, *Physical Review Letters*, Vol: 123, Pages: 040401-1-040401-6, ISSN: 0031-9007

In the classical domain, it is well known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely positive divisible quantum processes can still involve non-Markovian temporal correlations, that we then fully classify using the recently developed process tensor formalism, which generalizes the theory of stochastic processes to the quantum domain.

Zhang A, Xu H, Xie J,
et al., 2019, Experimental test of contextuality in quantum and classical systems, *Physical Review Letters*, Vol: 122, ISSN: 0031-9007

Contextuality is considered as an intrinsic signature of nonclassicality and a crucial resource for achieving unique advantages of quantum information processing. However, recently, there have been debates on whether classical fields may also demonstrate contextuality. Here, we experimentally configure a contextuality test for optical fields, adopting various definitions of measurement events, and analyze how the definitions affect the emergence of nonclassical correlations. The heralded single-photon state, which is a typical nonclassical light field, manifests contextuality in our setup; whereas contextuality for classical coherent fields strongly depends on the specific definition of measurement events, which is equivalent to filtering the nonclassical component of the input state. Our results highlight the importance of the definition of measurement events to demonstrate contextuality, and they link the contextual correlations to nonclassicality defined by quasiprobabilities in phase space.

Banchi L, Kolthammer WS, Kim MS, 2018, Multiphoton tomography with linear optics and photon counting, *Physical Review Letters*, Vol: 121, ISSN: 0031-9007

Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multimode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though nonuniversal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is saturated with random linear optics configurations, such as when the corresponding unitary transformation is Haar random. Furthermore, we show that for N photons, any unitary 2N design can be used to derive an analytical, though nonoptimal, state reconstruction protocol.

Yadin B, Binder FC, Thompson J,
et al., 2018, Operational resource theory of continuous-variable nonclassicality, *Physical Review X*, Vol: 8, ISSN: 2160-3308

Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P representation—a state lacking a positive P function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These measures lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multimode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single-mode Gaussian states.

Tang H, Di Franco C, Shi ZY,
et al., 2018, Experimental quantum fast hitting on hexagonal graphs, *Nature Photonics*, Vol: 12, Pages: 754-758, ISSN: 1749-4885

Quantum walks are powerful kernels in quantum computing protocols, and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on glued trees1, which demonstrate faster hitting performances than classical random walks. However, their experimental implementation is challenging, as this involves highly complex arrangements of an exponentially increasing number of nodes. Here, we propose an alternative structure with a polynomially increasing number of nodes. We successfully map such graphs on quantum photonic chips using femtosecond-laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on graphs with up to 160 nodes and a depth of eight layers, achieving a linear relationship between the optimal hitting time and the network depth. Our results open up a scalable path towards quantum speed-up in classically intractable complex problems.

Lubasch M, Valido AA, Renema JJ,
et al., 2018, Tensor network states in time-bin quantum optics, *Physical Review A*, Vol: 97, ISSN: 1050-2947

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

Kwon H, Jeong H, Jennings D,
et al., 2018, Clock-Work Trade-Off Relation for Coherence in Quantum Thermodynamics, *PHYSICAL REVIEW LETTERS*, Vol: 120, ISSN: 0031-9007

In thermodynamics, quantum coherences—superpositions between energy eigenstates—behave in distinctly nonclassical ways. Here we describe how thermodynamic coherence splits into two kinds—“internal” coherence that admits an energetic value in terms of thermodynamic work, and “external” coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence, we provide dynamical constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clock–work trade-off relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system.

Rigovacca L, Kolthammer WS, Franco CD,
et al., 2018, Optical nonclassicality test based on third-order intensity correlations, *Physical Review A*, Vol: 97, ISSN: 1050-2947

We develop a nonclassicality criterion for the interference of three delayed,but otherwise identical, light fields in a three-mode Bell interferometer. Wedo so by comparing the prediction of quantum mechanics with those of aclassical framework in which independent sources emit electric fields withrandom phases. In particular, we evaluate third-order correlations among output intensities as a function of the delays, and show how the presence of a correlation revival for small delays cannot be explained by the classical model of light. The observation of a revival is thus a nonclassicality signature, which can be achieved only by sources with a photon-number statistics that is highly sub-Poissonian. Our analysis provides strong evidence for the nonclassicality of the experiment discussed in [Menssen et al., PRL, 118, 153603 (2017)], and shows how a collective "triad" phase affects the interference of any three or more light fields, irrespective of their quantum or classical character.

Rigovacca L, Kato G, Bauml S,
et al., 2018, Versatile relative entropy bounds for quantum networks, *New Journal of Physics*, Vol: 20, ISSN: 1367-2630

We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel.

Bose S, Mazumdar A, Morley GW,
et al., 2017, Spin Entanglement Witness for Quantum Gravity, *Physical Review Letters*, Vol: 119, ISSN: 0031-9007

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

Dieleman F, Tame MS, Sonnefraud Y,
et al., 2017, Experimental Verification of Entanglement Generated in a Plasmonic System., *Nano Letters*, Vol: 17, Pages: 7455-7461, ISSN: 1530-6984

A core process in many quantum tasks is the generation of entanglement. It is being actively studied in a variety of physical settings-from simple bipartite systems to complex multipartite systems. In this work we experimentally study the generation of bipartite entanglement in a nanophotonic system. Entanglement is generated via the quantum interference of two surface plasmon polaritons in a beamsplitter structure, i.e., utilizing the Hong-Ou-Mandel (HOM) effect, and its presence is verified using quantum state tomography. The amount of entanglement is quantified by the concurrence and we find values of up to 0.77 ± 0.04. Verifying entanglement in the output state from HOM interference is a nontrivial task and cannot be inferred from the visibility alone. The techniques we use to verify entanglement could be applied to other types of photonic system and therefore may be useful for the characterization of a range of different nanophotonic quantum devices.

Armata F, Calajo G, Jaako T,
et al., 2017, Harvesting Multiqubit Entanglement from Ultrastrong Interactions in Circuit Quantum Electrodynamics, *Physical Review Letters*, Vol: 119, ISSN: 0031-9007

We analyze a multi-qubit circuit QED system in the regime where the qubit-photon couplingdominates over the system’s bare energy scales. Under such conditions a manifold of low-energystates with a high degree of entanglement emerges. Here we describe a time-dependent protocol forextracting these quantum correlations and converting them into well-defined multi-partite entangledstates of non-interacting qubits. Based on a combination of various ultrastrong-coupling effects theprotocol can be operated in a fast and robust manner, while still being consistent with experimentalconstraints on switching times and typical energy scales encountered in superconducting circuits.Therefore, our scheme can serve as a probe for otherwise inaccessible correlations in strongly-coupledcircuit QED systems. It also shows how such correlations can potentially be exploited as a resourcefor entanglement-based applications.

Armata F, Latmiral L, Plato ADK,
et al., 2017, Quantum limits to gravity estimation with optomechanics, *Physical Review A*, Vol: 96, ISSN: 1050-2947

We present a table-top quantum estimation protocol to measure the gravitational acceleration g by using an optomechanical cavity. In particular, we exploit the nonlinear quantum light-matter interaction between an optical field and a massive mirror acting as mechanical oscillator. The gravitational field influences the system dynamics affecting the phase of the cavity field during the interaction. Reading out such a phase carried by the radiation leaking from the cavity, we provide an estimate of the gravitational acceleration through interference measurements. Contrary to previous studies, having adopted a fully quantum description, we are able to propose a quantum analysis proving the ultimate bound to the estimability of the gravitational acceleration and verifying optimality of homodyne detection. Noticeably, thanks to the light-matter decoupling at the measurement time, no initial cooling of the mechanical oscillator is demanded in principle.

Wan KH, Dahlsten O, Kristjansson H,
et al., 2017, Quantum generalisation of feedforward neural networks, *npj Quantum Information*, Vol: 3, ISSN: 2056-6387

We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise are called feedforward, and have step-function activation functions). The quantum network can be trained efficiently using gradient descent on a cost function to perform quantum generalisations of classical tasks. We demonstrate numerically that it can: (i) compress quantum states onto a minimal number of qubits, creating a quantum autoencoder, and (ii) discover quantum communication protocols such as teleportation. Our general recipe is theoretical and implementation-independent. The quantum neuron module can naturally be implemented photonically.

Barnett SM, Beige A, Ekert A,
et al., 2017, Journeys from quantum optics to quantum technology, *PROGRESS IN QUANTUM ELECTRONICS*, Vol: 54, Pages: 19-45, ISSN: 0079-6727

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.

Browne D, Bose S, Mintert F,
et al., 2017, From quantum optics to quantum technologies, *Progress in Quantum Electronics*, Vol: 54, Pages: 2-18, ISSN: 0079-6727

Quantum optics is the study of the intrinsically quantum properties of light. During the second part of the 20th century experimental and theoretical progress developed together; nowadays quantum optics provides a testbed of many fundamental aspects of quantum mechanics such as coherence and quantum entanglement. Quantum optics helped trigger, both directly and indirectly, the birth of quantum technologies, whose aim is to harness non-classical quantum effects in applications from quantum key distribution to quantum computing. Quantum light remains at the heart of many of the most promising and potentially transformative quantum technologies. In this review, we celebrate the work of Sir Peter Knight and present an overview of the development of quantum optics and its impact on quantum technologies research. We describe the core theoretical tools developed to express and study the quantum properties of light, the key experimental approaches used to control, manipulate and measure such properties and their application in quantum simulation, and quantum computing.

Lv D, An S, Um M,
et al., 2017, Reconstruction of the Jaynes-Cummings field state of ionic motion in a harmonic trap, *PHYSICAL REVIEW A*, Vol: 95, ISSN: 2469-9926

A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum technologies. One of the most fundamental interaction models in quantum optics is the so-called Jaynes-Cummings model (JCM), which has been massively studied theoretically and experimentally. However, the expected essential dynamics of the field states under the resonant JCM has not been observed experimentally due to the lack of a proper reconstruction scheme. In this paper, we further develop a highly efficient vacuum measurement scheme and study the JCM dynamics in a trapped ion system with the capability of the vacuum measurement to reconstruct its quasiprobability Q function, which is a preferred choice to study the core of the dynamics of a quantum state in phase space. During the JCM dynamics, the Gaussian peak of the initial coherent state bifurcates and rotates around the origin of phase space. They merge at the so-called revival time at the other side of phase space. The measured Q function agrees with the theoretical prediction. Moreover, we reconstruct the Wigner function by deconvoluting the Q function and observe the quantum interference in the Wigner function at half of the revival time, where the vibrational state becomes nearly disentangled from the internal energy states and forms a superposition of two composite states. The scheme can be applied to other physical setups including cavity or circuit-QED and optomechanical systems.

Bose S, Wan C, Scala M,
et al., 2017, Comment on "Matter-Wave Interferometry of a Levitated Thermal Nano-Oscillator Induced and Probed by a Spin" Reply, *PHYSICAL REVIEW LETTERS*, Vol: 118, ISSN: 0031-9007

Rashid M, Tufarelli T, Bateman J,
et al., 2016, Experimental realization of a thermal squeezed state of levitated optomechanics, *Physical Review Letters*, Vol: 117, ISSN: 1079-7114

We experimentally squeeze the thermal motional state of an optically levitated nanosphere by fast switching between two trapping frequencies. The measured phase-space distribution of the center of mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and, even after squeezing, the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could, in principle, be achieved by repeating the frequency-switching protocol multiple times.

Rigovacca L, Franco CD, Metcalf BJ,
et al., 2016, Non-Classicality Criteria in Multi-port Interferometry, *Physical Review Letters*, Vol: 117, ISSN: 1079-7114

Quantum interference lies at the basis of fundamental differences betweenquantum and classical behaviors. It is thus crucial to understand theboundaries between what interference patterns can be described by classicalwave mechanics and what, on the other hand, can only be understood with aproper quantum mechanical description. While a lot of work has already beendone for the simple case of two-mode interference, the multi-mode case has notbeen fully explored yet. Here we derive bounds for classical models of lightfields in a general scenario of intensity interferometry, and we show how theycan be violated in a quantum framework. As a consequence, this violation actsas a non-classicality witness, able to detect the presence of sources withsub-Poissonian photon-number statistics. We also derive a criterion forcertifying the indivisibility of a quantum interferometer and obtain a methodto simultaneously measure the average pairwise distinguishability of the inputsources.

Facchi P, Kim MS, Pascazio S,
et al., 2016, Bound states and entanglement generation in waveguide quantum electrodynamics, *PHYSICAL REVIEW A*, Vol: 94, ISSN: 2469-9926

Kim MS, Wan C, Scala M,
et al., 2016, Free nano-object Ramsey interferometry for large quantum superpositions, *Physical Review Letters*, Vol: 117, ISSN: 1079-7114

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity.The motion of the center of mass (c.m.) of the free object is coupled to its internal spin systemmagnetically, and a free ight scheme is developed based on coherent spin control. The wavepacketof the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale.A gravity induced dynamical phase (accrued solely on the spin state, and measured through aRamsey scheme) is used to reveal the above spatially delocalised superposition of the spin-nano-object composite system that arises during our scheme. We nd a remarkable immunity to themotional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamicaldecoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramseyfringes. The mass independence of our scheme makes it viable for a nano-object selected from anensemble with a high mass variability. Given these advantages, a quantum superposition with 100nm spatial separation for a massive object of 10⁹ amu is achievable experimentally, providing a routeto test postulated modi cations of quantum theory such as continuous spontaneous localisation.

Boutari J, Feizpour A, Barz S,
et al., 2016, Large scale quantum walks by means of optical fiber cavities, *Journal of Optics*, Vol: 18, ISSN: 2040-8986

We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show that this platform can achieve very low losses combined with high-fidelity operations, enabling an unprecedented large number of steps in a passive system, as required for scenarios with multiple walkers. Furthermore the platform is reconfigurable, enabling variation of the coin, and readily extends to multidimensional lattices. We demonstrate variation of the coin bias experimentally for three different values.

Armata F, Latmiral L, Pikovski I,
et al., 2016, Quantum and Classical Phases in Optomechanics, *Physical Review A*, Vol: 93, ISSN: 1094-1622

The control of quantum systems requires the ability to change and read-outthe phase of a system. The non-commutativity of canonical conjugate operatorscan induce phases on quantum systems, which can be employed for implementingphase gates and for precision measurements. Here we study the phase acquired bya radiation field after its radiation pressure interaction with a mechanicaloscillator, and compare the classical and quantum contributions. The classicaldescription can reproduce the nonlinearity induced by the mechanical oscillatorand the loss of correlations between mechanics and optical field at certaininteraction times. Such features alone are therefore insufficient for probingthe quantum nature of the interaction. Our results thus isolate genuine quantumcontributions of the optomechanical interaction that could be probed in currentexperiments.

Milburn TJ, Kim MS, Vanner MR, 2016, Nonclassical-state generation in macroscopic systems via hybrid discrete-continuous quantum measurements, *Physical Review A*, Vol: 93, ISSN: 1094-1622

Nonclassical-state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum nondemolition quadrature measurements and single quanta addition or subtraction to prepare quantum superposition states in bosonic systems. The performance of each permutation is quantified and compared using several different nonclassicality criteria including Wigner negativity, nonclassical depth, and optimal fidelity with a coherent-state superposition. We also compare the performance of our protocol using squeezing instead of a quadrature measurement and find that the purification provided by the quadrature measurement can significantly increase the nonclassicality generated. Our approach is ideally suited for implementation in light-matter systems such as quantum optomechanics and atomic spin ensembles, and offers considerable robustness to initial thermal occupation.

Latmiral L, Armata F, Genoni MG,
et al., 2016, Probing anharmonicity of a quantum oscillator in an optomechanical cavity, *Physical Review A*, Vol: 93, ISSN: 1094-1622

We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation precision posed by quantum mechanics and compare it with the precision obtainable with feasible measurements such as homodyne and heterodyne detection on the cavity field. In particular we demonstrate that homodyne detection is nearly optimal in the limit of a large number of photons of the field and we discuss the estimation precision of small anharmonicities in terms of its signal-to-noise ratio.

Kim MS, Wan C, Scala M,
et al., 2016, Tolerance in the Ramsey interference of a trapped nanodiamond, *Physical Review A*, Vol: 93, ISSN: 1094-1622

The scheme recently proposed in [M. Scala et al., Phys Rev Lett 111, 180403 (2013)], where agravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trappednanodiamond by the interaction between its magnetic moment and the quantized motion of theparticle, provides a way to detect spatial quantum superpositions by means of spin measurementsonly. Here, the effect of unwanted coupling with other motional degrees of freedom is considered andwe show that it does not affect the validity of the scheme. Both this coupling and the additionalerror source due to misalignment between the quantization axis of the NV center spin and thetrapping axis are shown not to change the qualitative behavior of the system, so that a proof-ofprincipleexperiment can be neatly performed. Our analysis, which shows that the scheme retainsthe important features of not requiring ground state cooling and of being resistant to thermalfluctuations, can be useful for the several schemes which have been proposed recently for testingmacroscopic superpositions in trapped microsystems.

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