In this paper we propose a general method to quantify how "quantum" a set of quantum states is. The idea is to gauge the quantumness of the set by the worst-case difficulty of transmitting the states through a purely classical communication channel. Potential applications of this notion arise in quantum cryptography, where one might like to use an alphabet of states that promises to be the most sensitive to quantum eavesdropping, and in laboratory demonstrations of quantum teleportation, where it is necessary to check that quantum entanglement has actually been used in the protocol.
Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predi…
We introduce a method to witness the quantumness of a system. The method relies on the fact that the anticommutator of two classical states is always positive. We show that there is always a nonpositive anticommutator due to any two quantum states. We notice that interference depends on the trace of the anticommutator of two states and it is therefore more natural to detect quantumness by looking at anticommutators of states rather than their commutators.
We investigate the notion of quantumness based on the non-commutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition of a given composite system is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient …
Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its Schwinger two-photon realization are proposed as squeezed states. The physical implication of this assumption is that two additional degrees of freedom become available for the control of quantum optical systems. The resulting physical predictions are evaluated in terms of quadrature squeezing and photon statistics, while the application to a Mach-Zehnder in…
A state of a quantum systems can be regarded as {\it classical} ({\it quantum}) with respect to measurements of a set of canonical observables iff there exists (does not exist) a well defined, positive phase space distribution, the so called Galuber-Sudarshan $P$-representation. We derive a family of classicality criteria that require that averages of positive functions calculated using $P$-representation must be positive. For polynomial functions, these criteria are related to 17-th Hilbert's problem, and have physical meaning of generalized squeezing conditions; alternatively, they may be in…
We provide experimental evidence of quantum features in bi-partite states classified as entirely classical according to a conventional criterion based on the Glauber P-function but possessing non-zero Gaussian quantum discord. Their quantum nature is experimentally revealed by acting locally on one part of the discordant state. Adding an environmental system purifying the state, we unveil the flow of quantum correlations within a global pure system using the Koashi-Winter inequality. We experimentally verify and investigate the counterintuitive effect of discord increase under the action of lo…
Clarifying the impact of quantumness in the operation and properties of thermal machines represents a major challenge. Here we envisage a toy model acting either as an information-driven fridge or as heat-powered information eraser in which coherences can be naturally introduced in by means of squeezed thermal reservoirs. We study the validity of the transient entropy production fluctuation theorem in the model with and without squeezing as well as its decomposition into adiabatic and non-adiabatic contributions. Squeezing modifies fluctuations and introduces extra mechanisms of entropy exchan…
We present a technique for measuring the second-order coherence function $g^{(2)}(τ)$ of light using a Hanbury-Brown Twiss intensity interferometer modified for homodyne detection. The experiment was performed entirely in the continuous variable regime at the sideband frequency of a bright carrier field. We used the setup to characterize $g^{(2)}(τ)$ for thermal and coherent states, and investigated its immunity to optical loss. We measured $g^{(2)}(τ)$ of a displaced squeezed state, and found a best anti-bunching statistic of $g^{(2)}(0) = 0.11 \pm 0.18$.
Witnessing non-classicality in the gravitational field has been claimed to be practically impossible. This constitutes a deep problem, which has even lead some researchers to question whether gravity should be quantised, due to the weakness of quantum effects. To counteract these claims, we propose a thought experiment that witnesses non-classicality of a physical system by probing it with a qubit. Remarkably, this experiment does not require any quantum control of the system, involving only measuring a single classical observable on that system. In addition, our scheme does not even assume an…
Suppose one wants to certify that a quantum channel is not entanglement-breaking. I consider all four combinations of trusted and untrusted devices at the input and output of the channel, finding that the most interesting is a trusted preparation device at the input and an untrusted measurement device at the output. This provides a time-like analogue of EPR-steering, which turns out to reduce to the problem of joint measurability, connecting these concepts in a different way to other recent work. I suggest a few applications of this connection, such as a resource theory of incompatibility. Thi…
We propose a method to infer the single-particle entropy of bosonic atoms in an optical lattice and to study the local evolution of entropy, spin squeezing, and entropic inequalities for entanglement detection in such systems. This method is based on experimentally feasible measurements of non-nearest-neighbour coherences. We study a specific example of dynamically controlling atom tunneling between selected sites and show that this could potentially also improve the metrologically relevant spin squeezing.
We investigate the presence of spin- and planar- squeezing in generalized superpositions of atomic (or spin) coherent states (ACS). Spin-squeezing has been shown to be a useful tool in determining the presence of entanglement in multipartite systems, such as collections of two-level atoms, as well as being an indication of reduced projection noise and sub-shot-noise limited phase uncertainty in Ramsey spectroscopy, suitable for measuring phases $ϕ\sim 0$. On the other hand, planar-squeezed states display reduced projection noise in two directions simultaneously and have been shown to lead to e…
It is commonly agreed that the electromagnetic vacuum is not empty but filled with virtual photons. This leads to effects like Lamb shift and spontaneous emission. Here we argue that if the vacuum has virtual photons it might mean that it is very weakly squeezed and therefore the electromagnetic field is not in its ground state (vacuum) but in an excited dark state. We suggest a stringent test relying on measuring various properties of the electromagnetic field to exclude this yet-untested squeezing hypothesis. This could be done by measuring the number of photons as a function of frequency an…
The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas, the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach simultaneous three bipartite entanglements via the qu…
We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup only needs beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.
We propose to explore the quantum nature of gravity using the correlation of light between two optomechanical cavities, and the quantumness of the correlation is witnessed by squeezing. As long as the gravity between the end mirrors of two cavities is quantum in the Newtonian limit, we show that the squeezing is always nonzero and monotonically increases as the mechanical property of the mirrors is improved. The proposed scheme provides a new pathway for testing the quantum nature of gravity systematically with tabletop experiments.
We outline a new class of continuous-variable graph states that can be useful to describe entangle- ment, and also multimode squeezing, in an optical frequency comb. We show that a particular case of such states coincides with the squeezing of the carrier-envelope phase, or of the total intensity, of a mode-locked laser. We then discuss the experimental issues related to measuring the quantum noise of the carrier-envelope phase of a frequency comb and show that this can be carried out by use of quantum heterodyne multiplexing, a technique that may be useful to measure multipartite entanglement…
The universe is believed to be originated from a quantum state. However, defining measurable quantities for the quantum properties in the present universe has gained interest recently. In this submission, we propose a quantum Poincare sphere as an observable quantity that can hint at the quantumness of primordial gravitational waves and large-scale magnetic fields. The Poincare sphere is defined in terms of quantum stokes operators associated with the polarization of those fields, which can be measured directly. We have further studied the effects of the initial non-BD vacuum on the power spec…
We show that substantial quantum squeezing of mechanical motion can be achieved for micron-sized cantilever devices fabricated using available techniques. A method is also described for measuring the cantilever fluctuation magnitudes in the squeezing regime.
A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system.We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus' effective state, in the limit of a strong coarse-graining action - a…
We show how to control spatial quantum correlations in a multimode degenerate optical parametric oscillator type I below threshold by introducing a spatially inhomogeneous medium, such as a photonic crystal, in the plane perpendicular to light propagation. We obtain the analytical expressions for all the correlations in terms of the relevant parameters of the problem and study the number of photons, entanglement, squeezing, and twin beams. Considering different regimes and configurations we show the possibility to tune the instability thresholds as well as the quantumness of correlations by br…
Traveling wave parametric amplifiers (TWPAs) have recently emerged as essential tools for broadband near quantum-limited amplification. However, their use to generate microwave quantum states still misses an experimental demonstration. In this letter, we report operation of a TWPA as a source of two-mode squeezed microwave radiation. We demonstrate broadband entanglement generation between two modes separated by up to 400 MHz by measuring logarithmic negativity between 0.27 and 0.51 and collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. This work opens interesting p…
Twin-Signal-Recycling (TSR) builds on the resonance doublet of two optically coupled cavities and efficiently enhances the sensitivity of an interferometer at a dedicated signal frequency. We report on the first experimental realization of a Twin-Signal-Recycling Michelson interferometer and also its broadband enhancement by squeezed light injection. The complete setup was stably locked and a broadband quantum noise reduction of the interferometers shot noise by a factor of up to 4\,dB was demonstrated. The system was characterized by measuring its quantum noise spectra for several tunings of …
We show that the nanoresonator position can be squeezed significantly below the ground state level by measuring the nanoresonator with a quantum point contact or a single-electron transistor and applying a periodic voltage across the detector. The mechanism of squeezing is basically a generalization of quantum nondemolition measurement of an oscillator to the case of continuous measurement by a weakly coupled detector. The quantum feedback is necessary to prevent the ``heating'' due to measurement back-action. We also discuss a procedure of experimental verification of the squeezed state.
We propose and analyse a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realisations of the scheme may be tested with existing methods via measuremen…
Squeezed states can be employed for entanglement-based continuous-variable quantum key distribution, where the secure key rate is proportional to the bandwidth of the squeezing. We produced a non-classical continuous-wave laser field at the telecommunication wavelength of 1550 nm, which showed squeezing over a bandwidth of more than 2 GHz. The experimental setup used parametric down-conversion via a periodically poled potassium titanyl phosphate crystal (PPKTP). We did not use any resonant enhancement for the funda- mental wavelength, which should in principle allow a production of squeezed li…
While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglemen…
Momentum diffusion is a possible mechanism for driving macroscopic quantum systems towards classical behaviour. Experimental tests of this hypothesis rely on a precise estimation of the strength of this diffusion. We show that quantum-mechanical squeezing offers significant improvements, including when measuring position. For instance, with 10dB of mechanical squeezing, experiments would require a tenth of proposed free-fall times. Momentum measurement is better by an additional factor of three, while another quadrature is close to optimal. These have particular implications for the space-base…
A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light. Q…
The relationship between orientation-to-alignment conversion (a form of atomic polarization evolution induced by an electric field) and the phenomenon of spin squeezing is demonstrated. A "stretched" state of an atom or molecule with maximum angular-momentum projection along the quantization axis possesses orientation and is a quantum-mechanical minimum-uncertainty state, where the product of the equal uncertainties of the angular-momentum projections on two orthogonal directions transverse to the quantization axis is the minimum allowed by the uncertainty relation. Application of an electric …
In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary concept in their formalism was that it was fundamentally two-mode, i.e. the related observables could not be attributed to any single one of the comprising modes, but rather to a generalized complex quadrature that could only be attributed to both of them. Here, we propose a subtle, but fundamentally meaningful modification to their important work. Unlike the abo…
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that mea…
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any (2 x d) system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenom…
We demonstrate a transducer of nanomechanical motion based on cavity enhanced optical near-fields capable of achieving a shot-noise limited imprecision more than 10 dB below the standard quantum limit (SQL). Residual background due to fundamental thermodynamical frequency fluctuations allows a total imprecision 3 dB below the SQL at room temperature (corresponding to 600 am/Hz^(1/2) in absolute units) and is known to reduce to negligible values for moderate cryogenic temperatures. The transducer operates deeply in the quantum backaction dominated regime, prerequisite for exploring quantum back…
The radiation-pressure driven interaction of a coherent light field with a mechanical oscillator induces correlations between the amplitude and phase quadratures of the light. These correlations result in squeezed light -- light with quantum noise lower than shot noise in some quadratures, and higher in others. Due to this lower quantum uncertainty, squeezed light can be used to improve the sensitivity of precision measurements. In particular, squeezed light sources based on nonlinear optical crystals are being used to improve the sensitivity of gravitational wave (GW) detectors. For optomecha…
We discuss the quantum mechanical description of a gravitational wave interacting with a cavity electromagnetic field. Quantum fluctuations of the gravitational vacuum induce squeezing in the optical field. Moreover, this squeezing experiences revivals, a purely quantum effect. Measuring these gravitationally induced revivals, although out of reach from experiments, would provide evidence on the quantum nature of gravity. We also discuss the quantum mechanical treatment of the interaction between coherent and squeezed gravitational wave states and a gravity wave detector. In the case of a cohe…
I propose an efficient method for measuring non-linear coupling between the collective axial breathing mode and the radial rocking mode induced by the mutual Coulomb repulsion in linear ion crystal. The quantum sensing technique is based on the laser induced coupling between one of the vibrational modes and the internal ion's spin states which allows to estimate the non-linear coupling either by measuring the phonon probability distribution or directly be observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of non-linear phonon coupling the off-resonan…
We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold 87Rb probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor polarizability, whose irreducible components can be selected by means of probe detuning. The D1 and D2 lines of Rb are explored and we identify different detunings which lead to Hamiltonians with different symmetries for rotations. As possible applications of these Hamiltonians, we describe schemes for spin squeezing, quantum cloning, quantum memory, and measuring atom nu…
Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on 2D crystal arrays of approximately one hundred $^9$Be$^+$ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and …
In relation of observable and quantum state, the entity $I_C$ from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this article its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogat…
