We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B \textbf{1}, L9 (1999), and Braunstein and Kimble, \pra\textbf{61}, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolski-Rosen) beams is generated from two independent squeezed vacua. After adding two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement, our channel is superior to conventional channels such as coherent and squeezing channels. In addition, optical addition and subtraction processes demonstrated are elementary operations of universal quantum information processing on continuous variables.
We report on the efficient generation, propagation, and re-emission of squeezed long-range surface-plasmon polaritons (SPPs) in a gold waveguide. Squeezed light is used to excite the non-classical SPPs and the re-emitted quantum state is fully quantum characterized by complete tomographic reconstruction of the density matrix. We find that the plasmon-assisted transmission of non-classical light in metallic waveguides can be described by a Hamiltonian analogue to a beam splitter. This result is explained theoretically.
We report on the first experimental demonstration of purification of nonclassical continuous variable states. The protocol uses two copies of phase-diffused states overlapped on a beam splitter and provides Gaussified, less mixed states with the degree of squeezing improved. The protocol uses only linear optical devices such as beam splitters and homodyne detection, thereby proving these optical elements can be used for successful purification of this type of state decoherence which occurs in optical transmission channels.
We propose and experimentally demonstrate a universal quantum averaging process implementing the harmonic mean of quadrature variances. The harmonic mean protocol can be used to efficiently stabilize a set of fragile squeezed light sources with statistically fluctuating noise levels. The averaged variances are prepared probabilistically by means of linear optical interference and measurement induced conditioning. We verify that the implemented harmonic mean outperforms the standard arithmetic mean strategy. The effect of quantum averaging is experimentally tested both for uncorrelated and part…
Quantum teleportation of a squeezed state is demonstrated experimentally. Due to some inevitable losses in experiments, a squeezed vacuum necessarily becomes a mixed state which is no longer a minimum uncertainty state. We establish an operational method of evaluation for quantum teleportation of such a state using fidelity, and discuss the classical limit for the state. The measured fidelity for the input state is 0.85$\pm$ 0.05 which is higher than the classical case of 0.73$\pm$0.04. We also verify that the teleportation process operates properly for the nonclassical state input and its squ…
We report on the experimental combination of three advanced interferometer techniques for gravitational wave detection, namely power-recycling, detuned signal-recycling and squeezed field injection. For the first time we experimentally prove the compatibility of especially the latter two. To achieve a broadband non-classical sensitivity improvement we applied a filter cavity for compensation of quadrature rotation. Signal to noise ratio was improved by up to 2.8 dB beyond the coherent state's shot noise. The complete set-up was stably locked for arbitrary times and characterized by injected si…
We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing …
The sensitivity of laser interferometers used for the detection of gravitational waves (GWs) is limited by quantum noise of light. An improvement is given by light with squeezed quantum uncertainties, as employed in the GW detector GEO600 since 2010. To achieve simultaneous noise reduction at all signal frequencies, however, the spectrum of squeezed states needs to be processed by 100m-scale low-loss optical filter cavities in vacuum. Here, we report on the proof-of-principle of an interferometer setup that achieves the required processed squeezed spectrum by employing Einstein-Podolsky-Rosen …
Time coding quantum key distribution with coherent faint pulses is experimentally demonstrated. A measured 3.3 % quantum bit error rate and a relative contrast loss of 8.4 % allow a 0.49 bit/pulse advantage to Bob.
A prerequisite for universal quantum computation and other large-scale quantum information processors is the careful preparation of quantum states in massive numbers or of massive dimension. For continuous variable approaches to quantum information processing (QIP), squeezed states are the natural quantum resources, but most demonstrations have been based on a limited number of squeezed states due to the experimental complexity in up-scaling. The number of physical resources can however be significantly reduced by employing the technique of temporal multiplexing. Here, we demonstrate an applic…
We study the measurement-induced non-Gaussian operation on the single- and two-mode \textit{Gaussian} squeezed vacuum states with beam splitters and on-off type photon detectors, with which \textit{mixed non-Gaussian} states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are eff…
We report the experimental demonstration of polarization squeezed beam at 795 nm by combining a quadrature squeezed beam with a coherent beam. The quadrature squeezed beam is generated by a degenerate optical parametric amplifier based on a PPKTP crystal. Stokes parameter squeezing of -3.8 dB and anti squeezing of +5.0 dB is observed. This polarization squeezed beam resonant to rubidium D1 line has potential applications in quantum information networks and precise measurement beyond the shot noise limit.
We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8 non-orthogonal codeword states corresponding to the value of a block of three binary letters. We use quantum coding to compress this quantum data into a two-qubit quantum channel and then uncompress the two-qubit channel to restore the original data with a fidelity approaching the theoretical limit.
We demonstrate an unconditional high-fidelity teleporter capable of preserving the broadband entanglement in an optical squeezed state. In particular, we teleport a squeezed state of light and observe $-0.8 \pm 0.2$dB of squeezing in the teleported (output) state. We show that the squeezing criterion translates directly into a sufficient criterion for entanglement of the upper and lower sidebands of the optical field. Thus, this result demonstrates the first unconditional teleportation of broadband entanglement. Our teleporter achieves sufficiently high fidelity to allow the teleportation to b…
We study a continuous variable (CV) dense-coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense-coding prot…
We consider sub-Poissonian single-mode laser with external synchronization and analyze its applicability to the problems of quantum information. Using Heisenberg-Langevin theory we calculate the quadrature variances of the field emitted by this laser. It is shown that such systems can demonstrate strong quadrature squeezing. Taking into account that the emitted field is temporally multi-mode the application of such sources to multichannel quantum teleportation and dense coding protocols is discussed.
Besides quantum entanglement and steering, quantum coherence has also been identified as a useful quantum resource in quantum information. It is important to investigate the evolution of quantum coherence in practical quantum channels. In this paper, we experimentally quantify the quantum coherence of a squeezed state and a Gaussian Einstein-Podolsky-Rosen (EPR) entangled state transmitted in Gaussian thermal noise channel, respectively. By reconstructing the covariance matrix of the transmitted states, quantum coherence of these Gaussian states is quantified by calculating the relative entrop…
A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean …
Gaussian boson sampling (GBS) is quantum sampling task in which one has to draw samples from the photon-number distribution of a large-dimensional nonclassical squeezed state of light. In an effort to make this task intractable for a classical computer, experiments building GBS machines have mainly focused on increasing the dimensionality and squeezing strength of the nonclassical light. However, no experiment has yet demonstrated the ability to displace the squeezed state in phase-space, which is generally required for practical applications of GBS. In this work, we build a GBS machine which …
We analyze the effect of squeezing the channel in binary communication based on Gaussian states. We show that for coding on pure states, squeezing increases the detection probability at fixed size of the strategy, actually saturating the optimal bound already for moderate signal energy. Using Neyman-Pearson lemma for fuzzy hypothesis testing we are able to analyze also the case of mixed states, and to find the optimal amount of squeezing that can be effectively employed. It results that optimally squeezed channels are robust against signal-mixing, and largely improve the strategy power by comp…
We report on the demonstration of broadband squeezed laser beams that show a frequency dependent orientation of the squeezing ellipse. Carrier frequency as well as quadrature angle were stably locked to a reference laser beam at 1064nm. This frequency dependent squeezing was characterized in terms of noise power spectra and contour plots of Wigner functions. The later were measured by quantum state tomography. Our tomograph allowed a stable lock to a local oscillator beam for arbitrary quadrature angles with one degree precision. Frequency dependent orientations of the squeezing ellipse are ne…
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\leq4$, and conjecture that this can be generalized for an arbitrary $n$ Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimen…
We experimentally reconstruct Wigner's current of quantum phase space dynamics for the first time. We reveal the ``push-and-pull" associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only ``pulls" the system toward the origin of phase space, we also observe an outward ``push" because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeez…
A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down conversion in the limit of large gain to attain high efficiency. For a constraint in the mean number of photons n associated with modulation in the signal channel, the channel capacity for dense coding is found to be ln(1+n+n^2), which always beats coherent-state communication and surpasses squeezed-state communication for n>1. For n>>1, the dense coding capacity approaches twice that of either sche…
We show the equivalence between two different communication schemes that employ a couple of modes of the electromagnetic field. One scheme uses unconventional heterodyne detection, with correlated signal and image-band modes in a twin-beam state from parametric downconversion. The other scheme is realized through a complex-number coding over quadrature-squeezed states of two uncorrelated modes, each detected by ordinary homodyning. This equivalence concerns all the stages of the communication channel: the encoded state, the optimal amplifier for the channel, the master equation modeling the lo…
We establish a security proof of frequency-time coding quantum key distribution (FT-QKD) protocol by showing its connection to the squeezed state quantum key distribution protocol, which has been proven to be unconditionally secure. We also extend the prepare-and-measure FT-QKD protocol to an entanglement based FT-QKD protocol which is more appealing in practice. Furthermore, we propose a correlated frequency measurement scheme of entangled photon pair by using time resolving single photon detector. Simulation results show that the FT-QKD protocol can be implemented with today's technology.
Quantum optics experiments on "bright" beams typically probe correlations between side-band modes. However the extra degree of freedom represented by this dual mode picture is generally ignored. We demonstrate the experimental operation of a device which can be used to separate the quantum side-bands of an optical field. We use this device to explicitly demonstrate the quantum entanglement between the side-bands of a squeezed beam.
Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this paper, we give a formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters and birefly discuss how the results can apply to quantum information theory.
We consider the problem of evaluating the entanglement of non-Gaussian mixed states generated by photon subtraction from entangled squeezed states. The entanglement measures we use are the negativity and the logarithmic negativity. These measures possess the unusual property of being computable with linear algebra packages even for high-dimensional quantum systems. We numerically evaluate these measures for the non-Gaussian mixed states which are generated by photon subtraction with on/off photon detectors. The results are compared with the behavior of certain operational measures, namely the …
We investigate the prospects of using two-mode intensity squeezed twin-beams, generated in Rb vapor, to improve the sensitivity of spectroscopic measurements by engaging two-photon Raman transitions. As a proof of principle demonstration, we demonstrated the quantum-enhanced measurements of the Rb $5D_{3/2}$ hyperfine structure with reduced requirements for the Raman pump laser power and Rb vapor number density.
Squeezed states of light have been improving the sensitivity of gravitational-wave observatories and are nonclassical resources of quantum cryptography and envisioned photonic quantum computers. The higher the squeeze factor is, the higher is the quantum advantage. Almost all applications of squeezed light require multi-path optical interference, whose unavoidable imperfections introduce optical loss, degrade the squeeze factor, as well as the quantum advantage. Here, for the first time, we experimentally demonstrate the distillation of Gaussian squeezed states that suffered from Gaussian phot…
We report demonstrations of both quadrature squeezed vacuum and photon number difference squeezing generated in an integrated nanophotonic device. Squeezed light is generated via strongly driven spontaneous four-wave mixing below threshold in silicon nitride microring resonators. The generated light is characterized with both homodyne detection and direct measurements of photon statistics using photon number-resolving transition edge sensors. We measure $1.0(1)$~dB of broadband quadrature squeezing (${\sim}4$~dB inferred on-chip) and $1.5(3)$~dB of photon number difference squeezing (${\sim}7$…
We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We conclude that the requirements for a strong demonstration are not as stringent as previously thought and are within the reach of present technology.
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light fields. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U.L. Andersen [\pra {\bf 71}, 042308 (2005)], solely based on offline squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying t…
By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys. Rev. A {\bf 71}, 042308 (2005) \cite{Filip05.pra}), we experimentally demonstrate a universal, deterministic and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a …
We report the experimental demonstration of coherent control with high power, broadband squeezed vacuum. Although incoherent and exhibiting the statistics of a thermal noise, broadband squeezed vacuum is shown to induce certain two-photon interactions as a coherent ultrashort pulse with the same spectral bandwidth. Utilizing pulse-shaping techniques we coherently control the sum-frequency generation of broadband squeezed vacuum over a range of two orders of magnitude. Coherent control of two-photon interactions with broadband squeezed vacuum can potentially obtain spectral resolutions and exti…
In a new branch of quantum computing, information is encoded into coherent states, the primary carriers of optical communication. To exploit it, quantum bits of these coherent states are needed, but it is notoriously hard to make superpositions of such continuous-variable states. We have realized the complete engineering and characterization of a qubit of two optical continuous-variable states. Using squeezed vacuum as a resource and a special photon subtraction technique, we could with high precision prepare an arbitrary superposition of squeezed vacuum and a squeezed single photon. This coul…
We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion (E.G. Cavalcanti and M. Reid, Phys. Rev. Lett. 97, 170405 (2006)). The macroscopic coherence stems from interference between macroscopically distinct states in phase space and we prove experimentally that even the vacuum state contains these features with a distance in phase space of $0.51\pm0.02$ shot noise units (SNU). For squeezed states we found macroscopic superpositions with a distance of up to $0.83\pm0.02$ SNU. The proof of macroscopic quantum coherence was inv…
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$,…
We propose a scheme which encodes information in both the longitudinal and spatial transverse phases of a continuous-wave optical beam. A split detector-based interferometric scheme is then introduced to optimally detect both encoded phase signals. In contrast to present-day optical storage devices, our phase coding scheme has an information storage capacity which scales with the power of the read-out optical beam. We analyse the maximum number of encoding possibilities at the shot noise limit. In addition, we show that using squeezed light, the shot noise limit can be overcome and the number …
The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems as promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings and thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles to observe squeezing for gi…
We review our most recent results on application of the photon subtraction technique for optical quantum information processing primitives, in particular entanglement distillation and generation of squeezed qubit states. As an introduction we provide a brief summary of other experimental accomplishments in the field.
We demonstrate theoretically, and confirm experimentally, that nonlinear spin waves excited in thin yttrium iron garnet films are good candidates for squeezing vacuum quantum noise. The experimental demonstration is in the form of a measurement of spin-wave induced modulation instability (IMI) conducted in the classical regime. The experiment evidences strong phase locking of an idler wave parametrically generated in the film with a deterministic small-signal wave launched into the film from an external source. The theory predicts that the same behaviour will be observed for vacuum quantum noi…
A technique is demonstrated that allows free space atomic fountain clocks and interferometers to utilize optical cavity generated spin-squeezed states with over $390\,000$ ${}^{87}\text{Rb}$ atoms. Fluorescence imaging is used for population spectroscopy, after a free fall time of 4 milliseconds, to resolve a single-shot phase sensitivity of $814 (61)$ microradians, which is $5.8(0.6)$ decibels (dB) below the quantum projection limit. The dynamic range is observed to be 100 milliradians. When operating as a microwave atomic clock with $240\,000$ atoms at a 3.6 ms Ramsey time, a single-shot fra…
Beam alignment is an important practical aspect of the application of squeezed states of light. Misalignments in the detection of squeezed light result in a reduction of the observable squeezing level. In the case of squeezed vacuum fields that contain only very few photons, special measures must be taken in order to sense and control the alignment of the essentially dark beam. The GEO600 gravitational wave detector employs a squeezed vacuum source to improve its detection sensitivity beyond the limits set by classical quantum shot noise. Here, we present our design and implementation of an al…
A quantum channel is derived for continuous variable teleportation which is performed by means of an arbitrary entangled state and the standard protocol. When a Gaussian entangled state such as a two-mode squeezed-vacuum state is used, the continuous variable teleportation is equivalent to the thermalizing quantum channel. Continuous variable dense coding is also considered. Both the continuous variable teleportation and the continuous variable dense coding are characterized by the same function determined by the entangled state and the quantum measurement.
Squeezed light enables measurements with sensitivity beyond the quantum noise limit (QNL) for optical techniques such as spectroscopy, gravitational wave detection, magnetometry and imaging. Precision of a measurement -- as quantified by the variance of repeated estimates -- has also been enhanced beyond the QNL using squeezed light. However, sub-QNL sensitivity is not sufficient to achieve sub-QNL precision. Furthermore, demonstrations of sub-QNL precision in estimating transmission have been limited to picowatts of probe power. Here we demonstrate simultaneous enhancement of precision and se…
We analyse a novel squeezing and entangling mechanism which is due to correlated Stokes and anti-Stokes photon forward scattering in a multi-level atom vapour. Following the proposal we present an experimental demonstration of 3.5 dB pulsed frequency nondegenerate squeezed (quadrature entangled) state of light using room temperature caesium vapour. The source is very robust and requires only a few milliwatts of laser power. The squeezed state is generated in the same spatial mode as the local oscillator and in a single temporal mode. The two entangled modes are separated by twice the Zeeman fr…
Adopting quantum communication to modern networking requires transmitting quantum information through fiber-based infrastructure. We report the first demonstration of superdense coding over optical fiber links, taking advantage of a complete Bell-state measurement enabled by time-polarization hyperentanglement, linear optics, and common single-photon detectors. We demonstrate the highest single-qubit channel capacity to date utilizing linear optics, $1.665 \pm 0.018$, and we provide a full experimental implementation of a hybrid, quantum-classical communication protocol for image transfer.
Optimizing the physical realization of quantum gates is important to build a quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate $\mathcal{P}$ of the quantum Fredkin gate in our expe…
We report the demonstration of a magnetometer with noise-floor reduction below the shot-noise level. This magnetometer, based on a nonlinear magneto-optical rotation effect, is enhanced by the injection of a squeezed vacuum state into its input. The noise spectrum shows squeezed noise reduction of about 2 dB spanning from close to 100 Hz to several megahertz. We also report on the observation of two different regimes of operation of such a magnetometer: one in which the detection noise is limited by the quantum noise of the light probe only, and one in which we see additional noise originating…
We show that it is possible to transfer two-bit information via encoding a single qubit in a conventional nuclear magnetic resonance (NMR) experiment with two very weakly polarized nuclear spins. Nevertheless, the experiment can not be regarded as a demonstration of superdense coding by means of NMR because it is based on the large number of molecules being involved in the ensemble state rather than the entanglement of the NMR states. Following the discussions, an entanglement witness, particularly applicable for NMR, is introduced based on separate and simultaneous measurement of the individu…
Squeezed light is a critical resource in quantum sensing and information processing. Due to the inherently weak optical nonlinearity and limited interaction volume, considerable pump power is typically needed to obtain efficient interactions to generate squeezed light in bulk crystals. Integrated photonics offers an elegant way to increase the nonlinearity by confining light strictly inside the waveguide. For the construction of large-scale quantum systems performing many-photon operations, it is essential to integrate various functional modules on a chip. However, fabrication imperfections an…
