Skip to main content
NCBI home page
Scientific Reports logoLink to Scientific Reports
. 2015 Oct 15;5:15125. doi: 10.1038/srep15125

Qubit-Programmable Operations on Quantum Light Fields

Marco Barbieri 1,a, Nicolò Spagnolo 2, Franck Ferreyrol 3, Rémi Blandino 4, Brian J Smith 5, Rosa Tualle-Brouri 6
PMCID: PMC4606785  PMID: 26468614

Abstract

Engineering quantum operations is a crucial capability needed for developing quantum technologies and designing new fundamental physics tests. Here we propose a scheme for realising a controlled operation acting on a travelling continuous-variable quantum field, whose functioning is determined by a discrete input qubit. This opens a new avenue for exploiting advantages of both information encoding approaches. Furthermore, this approach allows for the program itself to be in a superposition of operations, and as a result it can be used within a quantum processor, where coherences must be maintained. Our study can find interest not only in general quantum state engineering and information protocols, but also details an interface between different physical platforms. Potential applications can be found in linking optical qubits to optical systems for which coupling is best described in terms of their continuous variables, such as optomechanical devices.

Control of quantum systems is a key task for any implementation of quantum technologies, as well as for fundamental quantum physics tests1. Quantum optics, despite the fact that nonlinear interactions are extremely challenging to achieve for few-photon-level quantum light, has made considerable progress thanks to the adoption of measurement-induced nonlinearities2. This technique for inducing nonlinear behaviour in otherwise linear systems consists in utilising ancillary resources, and then perform conditional operations based on the outcome of a measurement on a part of the whole system. It has been primarily applied to the implementation of quantum gates for qubits encoded in single-photon degrees of freedom3,4,5,6,7,8.

Recent developments have shown that the same idea can be exploited for more elaborate control, when it is the state of the quantum field itself that is manipulated through heralding measurements9,10. This is the case, for instance, of the operation of quantum gates in coherent-state quantum computing11,12,13,14, entanglement distillation15,16, photon addition and subtraction17,18,19 related to the production of finite-dimensional quantum states20,21, and noiseless amplification22,23,24,25. A new hybrid approach has built up from these investigations that aims at merging the advantages of a continuous-variable approach to quantum optics, with experimental and conceptual tools proper to single-photon manipulation, and viceversa26,27,28,29,30.

In this paper, we propose a different kind of interface between these two approaches in the concept of qubit-programmed operations on a quantum field. Our proposal extends current methods for implementing photon addition and subtraction to operate with an arbitrary superposition, whose parameters can be set conditionally on the logical state of a qubit, encoded in a degree of freedom of a single photon. In principle, our scheme can be embedded in a larger architecture: the program can be determined as the result of a former quantum computation, thus allowing the possibility of it being in a superposition state. The information processing is initially carried out on discrete variables, but it affects the state of the continuous variables quantum field. This solution is particularly appealing in that the program state can be prepared with high fidelity due to the current available methods for the manipulation of discrete-variable systems, including entangled states. These properties add new capabilities to the state engineering toolbox for quantum technologies.

Results

Qubit-controlled operations on continuous-variable fields

The general idea is illustrated in Fig. 1a: a quantum field, described by a state Inline graphic, is the target we aim at manipulating through an operation Inline graphic, set according to the instructions p we received from a second party; in other words, these instructions represent a programme that configures a particular choice of Inline graphic. In the most general case, Inline graphic will be represented as a coherent superposition of some elementary operations. Therefore, the programme will need to be in the form of a quantum state Inline graphic, so that a proper mapping can be applied. Differently from conditional gates, such as the controlled-NOT gate for two-qubits, we do not require that the programme state is preserved. Analogic control has been implemented using an optical displacement to modulate the probability amplitude of single-photon subtraction11,13,31, and extensions to optomechanics have been discussed32; here we analyse a scheme for implementing the interface between a quantum optical field and the simplest discrete programme, a qubit33.

Figure 1.

Figure 1

Open in a new tab

(a) Conceptual diagram of the programmable gate; (b) Experimental schematic of the programmable device indicating different interfering modes. BS1 has transmission coefficient t ~ 1. Output modes of the OPA and the single-photon source (SPS) are conveyed on the symmetric beamsplitter BS2. Polarisation-resolved detection is performed by means of photon-number resolving detectors (PNRDs).

At the basis of our proposal, there is the possibility of realising photon subtraction by means of a simple high-transmissivity beamsplitter, and photon addition by using an optical parametric amplifier (OPA) in the low-gain regime. These operations can only be implemented probabilistically, with a single photon acting as a herald: in the former case, this comes from the reflected mode, in the latter, from the idler mode of the OPA. It is also known that these events can be made indistinguishable by quantum interference, thus erasing the information as to whether the trigger signal originated from an addition or subtraction heralding photon34,35,36. Inspired by the setup for quantum teleportation, we can use a single photon to control the degree to which the erasure of information occurs. We notice that previous schemes for quantum state engineering, notably quantum scissors20,21, have made use of similar concepts, using a split single photon as the entangled resource.

Details of the protocol

Figure 1b details the apparatus of our proposal: consider the spatial mode 0 prepared in the n-photon Fock state Inline graphic, which constitutes the input to an OPA, driven in such conditions that well approximate photon addition. In terms of the two-mode interaction Inline graphic, this implies working in the regime of low parametric gain g ≪ 1. Further to the action of the OPA, the state is then passed through a high-transmissivity mirror (t2 ~ 1, r2 ≪ 1) that realises photon subtraction. The two heralding modes are superposed on the spatial mode 1, using two orthogonal polarisations: horizontal (H) for the subtraction herald, vertical (V) for the addition. The action of this device on Inline graphic gives the following expression for the output state:

graphic file with name srep15125-m9.jpg

obtained by invoking the canonical beam splitter transformations, as well as the disentangling theorem37. Here, we have used the notation C = cosh g, Γ = tanh g, with g the parametric gain, i.e. squeezing parameter.

Due to the correlations established between modes 0 and 1, any detection on the latter results in an effective operation applied to the input field; as an example, the detection of a single photon on mode 1 on the polarisation H (V) would herald realisation of photon subtraction (addition). Detection in the diagonal polarisation basis would erase the information about the origin of the photon. Thus the state on mode 0 is transformed with the equal superposition Inline graphic, and similarly for other choices of polarisation states, which can be readily obtained by suitable choice of optical elements34,35.

Our aim is to control the choice of superposition by programming it on a qubit in the form Inline graphic, i.e in the ‘dual-rail’ encoding: Inline graphic. To achieve our purpose, we herald the two optical modes 1 and 2 on a beamsplitter with transmission coefficient Inline graphic, and then herald on either the outcome Inline graphic or Inline graphic. In an ordinary teleportation experiment, this would correspond to selecting the singlet in a Bell-state analysis. Consequently, the state of mode 0 is projected to:

graphic file with name srep15125-m16.jpg

therefore, in the limit t ~ 1 and tuning the gain of the OPA so that Γ = rt−2, we can map the state of the qubit Inline graphic onto the heralded operator Inline graphic that acts on the input; detailed calculations are reported in the Supplementary Information. Based on the transformation Eq. (2), we can calculate the fidelity of the output states with the ideal case for different families of inputs. The results for four relevant cases Inline graphic, with a transmission t = 0.95, typical in such experiments11,14,38,39, is reported in Fig. 2.

Figure 2. Fidelity F(ρout, ρtarget(n)) of the output states ρout, as a function of the average photon number Inline graphic for four choices of the operator Inline graphic, and different families of input states ρin(n): coherent states Inline graphic with α real solid red), cat states Inline graphic (dashed blue), single-mode squeezed vacuum (dotted green).

Figure 2

Open in a new tab

We also include the case when U acts on a half of a two-mode squeezed state (dot-dashed purple). The transmission coefficient of the subtraction beamsplitter is t = 0.95.

Analysis of the process fidelity

While a reasonable level of fidelity can be reached at low photon numbers for different relevant classes of input states, the precise behaviour with respect to the ideal process operation depends on the specific class of input state. We can highlight two general observations: first, the quality of the approximate process implemented remains comparable to other conditional operations commonly performed (for Inline graphic)11,13,14,34,35. Remarkably, the fidelity for coherent states depends on the relative phase between the state and the operator. We have indeed verified that Inline graphic in all the reported range. Moreover, we observe that conditional process implemented on input states presenting a long tail in the photon number distribution, such as single-mode squeezed states, deviate more from the ideal targeted operation.

This occurrence can be understood by referring to the explicit form of the process tensor Inline graphic, where each term is defined as the probability amplitude for Inline graphic being transformed into Inline graphic40,41. In Fig. 3, our results for the process tensor associated with Inline graphic are compared with the ideal case Inline graphic. When observing the diagonal terms that govern the transfer of populations, Inline graphic, one observes that the main departure is the attenuation factor C−(n+1)tn−1, which is also responsible for the imbalance between the addition and subtraction terms.

Figure 3. Diagonal part of the process tensor Inline graphic for both the modelled process Eq. (2) with t = 0.95 (left), and the ideal Inline graphic operation (right).

Figure 3

Open in a new tab

Notice that, for ease of comparison, the modelled process tensor is rescaled by an overall factor 2/r2 due to the probabilistic nature of the process.

Robustness to experimental inefficiencies

Two main technical challenges must be met to achieve the proposed scheme. The first is associated with obtaining high-quality mode matching between signal and idler modes of the OPA34,35. This can be achieved by appropriately choosing the nonlinear interaction medium based upon its dispersion properties, and similarly well-chosen operating wavelength region to achieve degenerate phase matching associated with the photon addition process42,43,44,45. The second technical challenge to overcome is the limited detection efficiency of the heralding detectors. Numerical analysis of this effect has been examined for the process tensor Inline graphic, including the first-order corrections. However, we imagine to focus on operation in the high-efficiency regime, which has been achieved in recent demonstrations46,47,48.

The results of this analysis are summarised in Fig. 4, where we show a comparison of the process tensors for two values of the detection efficiency of the photon-number resolving detectors, η = 0.9 and η = 1 for the programme Inline graphic; full details on the form of the tensors are available in the Supplementary Information. For clarity of presentation, only a single heralding detection event associated with Inline graphic is considered, with the other events giving qualitatively similar results.

Figure 4. Comparison of the process tensor at different values of quantum efficiency of the detectors η, assumed equal for all involved.

Figure 4

Open in a new tab

Top: diagonal part of the process tensor Inline graphic. Bottom: section representative of the coherence transfer Inline graphic. For ease of comparison, the modelled process tensor is rescaled by an overall factor 4/r2 due to the probabilistic nature of the process.

The diagonal elements reveal that the attenuation at high photon number is more pronounced, since the inefficiency mainly results in the persistence of some population in original level Inline graphic. A minor effect consists in the transfer of population from Inline graphic to Inline graphic, in analogy with the results in Ref. 49. Further insight is provided by observing the terms governing the coherence between photon-number components of the output state. The inefficiency of the detection process induces an overall attenuation of the off-diagonal coherence terms. In fact, the detection can not discriminate perfectly between different photon-number states, resulting in an incoherent mixture of distinct contributions. This is similar to the heralding effects on conditional operations found recently in Fock-state filtration50. The sheer effect is a reduction of the maximal photon number at which a satisfactory fidelity can be found with respect the results reported in Fig. 2. This effect is captured more quantitatively in Fig. 5, in which we show the fidelities between targeted and modelled outputs for coherent state inputs at moderate average photon number Inline graphic. The protocol is resistant to small detection loss, η > 0.9 for Inline graphic, although it should be observed that these constraints will affect the overall success probability (see Supplementary Information).

Figure 5. Comparison of fidelities between the ideal and modelled outputs for coherent states inputs Inline graphic with α = 1 as a function of the transmission coefficient t and the detection efficiency η for Inline graphic and Inline graphic.

Figure 5

Open in a new tab

Discussion

We have presented a scheme for controlling the quantum state of a travelling light field conditioned on the logical state of a single optical qubit, which acts as a programme for a processing device. Our analysis highlights that a satisfactory fidelity, in excess of 95% can be achieved for a large class of states, in particular coherent states Inline graphic and cat states Inline graphic. We also investigate the effect of imperfect detection on the process, which reveal technical challenges for realistic devices and the input photon number limit threshold for reasonable process fidelity with the target operation. Continued progress in detection technology46,47,48 and quantum light sources45,51 will allow implementation of this protocol in the near future.

The present protocol could likely have application in implementing an interface between qubits and mesoscopic systems, such as optomechanical platforms52 or atomic ensembles53. On the one hand, our scheme delivers a single-mode continuous-variable coding of the original qubit. In the presence of Gaussian light-matter entanglement, which can be produced in these mesoscopic systems, an unconditional teleportation protocol can realise an efficient mapping of the state54. On the other, the controlled operation can be used to performed controlled non-Gaussian transformation, when acting upon the entangled light, with the possibility of enhancing or restoring the level of entanglement55. A more ambitious programme might look into the direct coupling of the light field to the mesoscopic field, for instance by using a stimulated Raman field56 in a memory, or stimulated second-harmonic generation in toroids57, as a strategy for producing controllable nonGaussian entanglement. At present, all these operation still require the engineering of mesoscopic systems with an acceptance bandwidth large enough to allow pulsed operation, a task which is under intense development58,59,60. In general, this interface might allow for more flexible control of quantum light, towards the investigation and the exploitation of micro-macro quantum correlations61,62,63.

Additional Information

How to cite this article: Barbieri, M. et al. Qubit-Programmable Operations on Quantum Light Fields. Sci. Rep. 5, 15125; doi: 10.1038/srep15125 (2015).

Supplementary Material

Supplementary Information
srep15125-s1.pdf (154.6KB, pdf)

Acknowledgments

We thank M. Karpinski, A. Datta, M. Cooper, I.A. Walmsley, and F. Sciarrino for discussion and encouragement. M.B. is supported by a Rita Levi-Montalcini fellowship of MIUR. N.S. is supported by the ERC-Starting Grant 3D-QUEST (grant agreement no. 307783, http://www.3dquest.eu). BJS was partially supported by the Oxford Martin School programme on Bio-Inspired Quantum Technologies. We acknowledge support from FIRB Futuro in Ricerca HYTEQ, the EPSRC (Grants No. EP/K034480/1, EP/K026534/1), the EC project SIQS, and the AFOSR EOARD.

Footnotes

Author Contributions M.B. and F.F. conceived the original idea, with input from R.B. and R.T.B. M.B. and N.S. refined the theory, with contributions from R.T.B. and B.J.S. and produced the code for generating the process matrices. All the authors discussed the results, and prepared the manuscript.

References

  1. Wiseman H. M. & Milburn G. J. Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009). [Google Scholar]
  2. Knill E., Laflamme R. & Milburn G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). [DOI] [PubMed] [Google Scholar]
  3. Pittman T. B. et al. Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys. Rev. A 68, 032316 (2003). [Google Scholar]
  4. O’Brien J. L. et al. Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003). [DOI] [PubMed] [Google Scholar]
  5. Gasparoni S. et al. Realization of a photonic controlled-NOT gate sufficient for quantum computation. Phys. Rev. Lett. 93, 020504 (2004). [DOI] [PubMed] [Google Scholar]
  6. Bao X.-H. et al. Optical Nondestructive Controlled-NOT Gate without Using Entangled Photons. Phys. Rev. Lett. 98, 170502 (2007). [Google Scholar]
  7. Lanyon B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys. 5, 134–140 (2009). [Google Scholar]
  8. Shadbolt P. J. et al. Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nature Photon. 6, 45–49 (2011). [Google Scholar]
  9. Ourjoumtsev A., Jeong H., Tualle-Brouri R. & Grangier P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007). [DOI] [PubMed] [Google Scholar]
  10. Bimbard E., Jain N., MacRae A. & Lvovsky A. I. Quantum-optical state engineering up to the two-photon level. Nature Photon. 4, 243–247 (2010). [Google Scholar]
  11. Neegaard-Nielsen J. S. et al. Optical Continuous-Variable Qubit. Phys. Rev. Lett. 105, 053602 (2010). [DOI] [PubMed] [Google Scholar]
  12. Marek P. & Fiurášek J. Elementary gates for quantum information with superposed coherent states. Phys. Rev. A 82, 014304 (2010). [Google Scholar]
  13. Tipsmark A. et al. Experimental demonstration of a Hadamard gate for coherent state qubits. Phys. Rev. A 84, 050301 (R) (2011). [Google Scholar]
  14. Blandino R. et al. Characterization of a π-phase shift quantum gate for coherent-state qubits. New J. Phys 14, 013017 (2012). [Google Scholar]
  15. Takahashi H. et al. Entanglement distillation from Gaussian input states. Nature Photon. 4, 178–181 (2010). [Google Scholar]
  16. Kurochkin Y., Prasad A. S. & Lvovsky A. I. Distillation of The Two-Mode Squeezed State. Phys. Rev. Lett. 112, 070402 (2014). [DOI] [PubMed] [Google Scholar]
  17. Zavatta A., Viciani S. & Bellini M. Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light. Science 306, 660–662 (2004). [DOI] [PubMed] [Google Scholar]
  18. Parigi V., Zavatta A., Kim M. S. & Bellini M. Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field. Science 317, 1890–1893 (2007). [DOI] [PubMed] [Google Scholar]
  19. Kumar R., Barrios E., Kupchak C. & Lvovsky A. I. Experimental Characterization of Bosonic Creation and Annihilation Operators. Phys. Rev. Lett. 110, 130403 (2013). [DOI] [PubMed] [Google Scholar]
  20. Pegg D. T., Phillips L. S. & Barnett S. M. Optical State Truncation by Projection Synthesis. Phys. Rev. Lett. 81, 1604 (1998). [Google Scholar]
  21. Lvovsky A. I. & Mlynek J. Quantum-Optical Catalysis: Generating Nonclassical States of Light by Means of Linear Optics. Phys. Rev. Lett. 88, 250401 (2002). [DOI] [PubMed] [Google Scholar]
  22. Xiang G. Y. et al. Heralded noiseless linear amplification and distillation of entanglement. Nature Photon. 4, 316–319 (2010). [Google Scholar]
  23. Ferreyrol F. et al. Implementation of a Nondeterministic Optical Noiseless Amplifier. Phys. Rev. Lett. 104, 123603 (2010). [DOI] [PubMed] [Google Scholar]
  24. Zavatta A., Fiurášek J. & Bellini M. A high-fidelity noiseless amplifier for quantum light states. Nature Photon. 5, 52–60 (2011). [Google Scholar]
  25. Usuga M. A. et al. Noise-powered probabilistic concentration of phase information. Nature Phys. 6, 767–771 (2010). [Google Scholar]
  26. Takeda S. et al. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature 500, 315–318 (2013). [DOI] [PubMed] [Google Scholar]
  27. Neergaard-Nielsen J. S. et al. Quantum tele-amplification with a continuous-variable superposition state. Nat. Photon. 7, 439–443 (2013). [Google Scholar]
  28. Jeong H. et al. Generation of hybrid entanglement of light. Nat. Photon. 8, 564–569 (2014). [Google Scholar]
  29. Morin O. et al. Remote creation of hybrid entanglement between particle-like and wave-like optical qubits. Nat. Photon. 8, 570–574 (2014). [Google Scholar]
  30. Donati G. et al. Observing optical coherence across Fock layers with weak-field homodyne detectors. Nat. Commun. 5, 5584 (2014). [DOI] [PubMed] [Google Scholar]
  31. Coelho A. S. et al. Universal state orthogonalizer and qubit generator. Preprint arXiv:1407:6644 (2014).
  32. Vanner M. R., Aspelmeyer M. & Kim M. S. Quantum State Orthogonalization and a Toolset for Quantum Optomechanical Phonon Control Phys. Rev. Lett. 110, 010504 (2013). [DOI] [PubMed] [Google Scholar]
  33. Fiuřásek J., Dušek M. & Filip R. Universal Measurement Apparatus Controlled by Quantum Software. Phys. Rev. Lett. 89, 190401 (2002). [DOI] [PubMed] [Google Scholar]
  34. Kim M. S., Jeong H., Zavatta A., Parigi V. & Bellini M. Scheme for Proving the Bosonic Commutation Relation Using Single-Photon Interference. Phys. Rev. Lett. 101, 260401 (2008). [DOI] [PubMed] [Google Scholar]
  35. Zavatta A., Parigi V., Kim M. S., Jeong H. & Bellini M. Experimental Demonstration of the Bosonic Commutation Relation via Superpositions of Quantum Operations on Thermal Light Fields. Phys. Rev. Lett. 103, 140406 (2009). [DOI] [PubMed] [Google Scholar]
  36. Lee S.-Y. & Nha H. Quantum state engineering by a coherent superposition of photon subtraction and addition. Phys. Rev. A 82, 053812 (2010). [Google Scholar]
  37. Collett M. J. Exact density-matrix calculations for simple open systems. Phys. Rev. A 38, 2233 (1988). [DOI] [PubMed] [Google Scholar]
  38. Wenger J., Tualle-Brouri R. & Grangier P. Non-Gaussian Statistics from Individual Pulses of Squeezed Light. Phys. Rev. Lett. 92, 153601 (2004). [DOI] [PubMed] [Google Scholar]
  39. Ourjoumtsev A., Tualle-Brouri R., Laurat J. & Grangier P. Generating Optical Schršdinger Kittens for Quantum Information Processing. Science 312, 83–86 (2006). [DOI] [PubMed] [Google Scholar]
  40. Lobino M. et al. Complete Characterization of Quantum-Optical Processes. Science 322, 563–566 (2008). [DOI] [PubMed] [Google Scholar]
  41. Rahimi-Keshari et al. Quantum process tomography with coherent states. New J. Phys. 13, 013006 (2011). [Google Scholar]
  42. Mosley P. J. et al. Heralded Generation of Ultrafast Single Photons in Pure Quantum States. Phys. Rev. Lett. 100, 133601 (2008). [DOI] [PubMed] [Google Scholar]
  43. Cohen O. et al. Tailored Photon-Pair Generation in Optical Fibers. Phys. Rev. Lett. 102, 123603 (2009). [DOI] [PubMed] [Google Scholar]
  44. Eckstein A., Brecht B. & Silberhorn C. A quantum pulse gate based on spectrally engineered sum frequency generation. Opt. Exp. 19, 13770–13778 (2011). [DOI] [PubMed] [Google Scholar]
  45. Spring J. B. et al. On-chip low loss heralded source of pure single photons. Opt Exp. 21, 13522–13532 (2013). [DOI] [PubMed] [Google Scholar]
  46. Marsili F. et al. Detecting single infrared photons with 93% system efficiency. Nature Photon. 7, 210–214 (2013). [Google Scholar]
  47. Divochiy A. et al. Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths. Nature Photon. 2, 302–306 (2008). [Google Scholar]
  48. Calkins B. et al. High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing. Opt. Exp. 21, 22657–22670 (2013). [DOI] [PubMed] [Google Scholar]
  49. Lee S. Y. & Nha H. Second-order superposition operations via Hong-Ou-Mandel interference. Phys. Rev. A 85, 043816 (2012). [Google Scholar]
  50. Cooper M., Slade E., Karpinski M. & Smith B. J. Characterization of conditional state-engineering quantum processes by coherent state quantum process tomography. New J. Phys. 17, 033041 (2015). [Google Scholar]
  51. Harder G. et al. An optimized photon pair source for quantum circuits. Opt. Exp. 21, 13975–13985 (2013). [DOI] [PubMed] [Google Scholar]
  52. Aspelmeyer M., Kippenberg T. J. & Marquardt F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014). [Google Scholar]
  53. Lvovsky A. I., Sanders B. C., Tittel W. Optical quantum memory. Nature Photon. 3, 706–714 (2009). [Google Scholar]
  54. Braunstein S. L. & Kimble H. J. Teleportation of continous quantum variables. Phys. Rev. Lett. 80, 869 (1998). [Google Scholar]
  55. Bartley T. J. & Walmsley I. A. Directly comparing entanglement-enhancing non-Gaussian operations. New J. Phys. 17, 023038 (2015). [Google Scholar]
  56. Datta A. et al. Compact continuous-variable entanglement distillation. Phys. Rev. Lett. 108, 060502 (2012). [DOI] [PubMed] [Google Scholar]
  57. Xuereb A., Barbieri M. & Paternostro M. Multipartite optomechanical entanglement from competing nonlinearities Phys. Rev. A 86, 013809 (2012). [Google Scholar]
  58. Vanner M. R. et al. Pulsed quantum optomechanics. Proc. Natl. Acad. Sci. USA 108, 16182–16187 (2011). [DOI] [PMC free article] [PubMed] [Google Scholar]
  59. Reim K. F. et al. Towards high-speed optical quantum memories. Nat. Photon. 4, 218 (2010). [Google Scholar]
  60. England et al. Storage and retrieval of THz-bandwidth single photons using a room-temperature diamond quantum memory. Phys. Rev. Lett. 114, 053602 (2015). [DOI] [PubMed] [Google Scholar]
  61. Bruno N. et al. Displacement of entanglement back and forth between the micro and macro domains. Nat. Phys. 9, 545–548 (2013). [Google Scholar]
  62. Lvovsky A. I. et al. Observation of microÐmacro entanglement of light. Nat. Phys. 9, 541–544 (2013). [Google Scholar]
  63. Kwon H. & Jeong H. Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state. Phys. Rev. A 91, 012340 (2015). [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Information
srep15125-s1.pdf (154.6KB, pdf)

Articles from Scientific Reports are provided here courtesy of Nature Publishing Group

RESOURCES