LETTERS PUBLISHED ONLINE: 7 NOVEMBER 2010 | DOI: 10.1038/NPHYS1819 Quantum memory for entangled continuous-variable states K. Jensen 1 † , W. Wasilewski 1 †‡ , H. Krauter 1 , T. Fernholz 1 ‡ , B. M. Nielsen 1 , M. Owari 2 , M. B. Plenio 2 , A. Serafini 3 , M. M. Wolf 1 and E. S. Polzik 1 * A quantum memory for light is a key element for the realization of future quantum information networks 1–3 . Requirements for a good quantum memory are versatility (allowing a wide range of inputs) and preservation of quantum information in a way unattainable with any classical memory device. Here we demonstrate such a quantum memory for continuous- variable entangled states, which play a fundamental role in quantum information processing 4–6 . We store an extensive alphabet of two-mode 6.0 dB squeezed states obtained by varying the orientation of squeezing and the displacement of the states. The two components of the entangled state are stored in two room-temperature cells separated by 0.5 m, one for each mode, with a memory time of 1 ms. The true quantum character of the memory is rigorously proved by showing that the experimental memory fidelity 0.52 ± 0.02 significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements. The continuous-variable regime represents one of the principal avenues towards the realization of quantum information processing and communication 4–6 . In the optical domain it operates with well-known optical modulation and detection techniques and allows for deterministic quantum operations. In the atomic domain it has been developed on the platform of atomic ensembles 2,3,7 . Advances in the realization of continuous-variable quantum protocols include unconditional quantum teleportation involving light 8 and atoms 9 , a number of results on memory 2,3,10,11 and quantum key distribution 12 . Hybrid continuous/discrete-variable operations 13–15 paving the road towards continuous-variable quantum computation 16,17 have also been reported. However, the ability to store non-classical continuous-variable states of light is crucial to enable further progress, in particular, for continuous-variable linear optics quantum computing with offline resources 17 , continuous-variable quantum repeaters 18,19 , entanglement-enhanced quantum metrology, iterative continuous- variable entanglement distillation 20 , continuous-variable cluster- state quantum computation 21 , communication/cryptography protocols involving several rounds 22 and quantum illumination 23 . Compared with a number of impressive results reporting discrete-variable quantum memories at the single-photon level (see reviews 1–3 and references therein), there have been very few experiments towards quantum memory for continuous- variable non-classical states. A fractional, 20 nsec, delay of 50 nsec pulsed continuous-variable entangled states in the atomic 1 Niels Bohr Institute, Danish Quantum Optics Center QUANTOP, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark, 2 Institut für Theoretische Physik, Universität Ulm, Albert-Einstein Allee 11, D-89069 Ulm, Germany, 3 University College London, Department of Physics and Astronomy, Gower Street, London WC1E 6BT, UK. † These authors contributed equally to this work. ‡ Present addresses: Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warszawa, Poland (W.W.); School of Physics and Astronomy, The University of Nottingham, University Park, Nottingham NG7 2RD, UK (T.F.). *e-mail:polzik@nbi.dk. vapour has recently been demonstrated 24 . Memory based on electromagnetically induced transparency for a squeezed vacuum state has been reported 25,26 , albeit with the fidelity below the classical benchmark 27 . Very recently, classical benchmarks for storing displaced squeezed states 28,29 have been derived, which made experimental implementation of such storage a timely challenge. Such states form an alphabet for continuous- variable quantum information encoding 16 . An exciting feature of displaced squeezed states is that the ratio of the quantum to classical fidelity grows inversely proportionally to the degree of squeezing. Here we report the realization of a quantum memory for a set of displaced two-mode squeezed states with an unconditionally high fidelity that exceeds the classical benchmark calculated on the basis of the method in ref. 28. The fidelity between the input state and the memory state is a sufficient condition for a memory or a teleportation protocol to be genuinely quantum. In fact, because continuous-variable protocols are deterministic, that is they have a unity efficiency, the fidelity becomes the preferred performance criterion. The experimental fidelity demonstrated here, which exceeds the classical benchmark fidelity, implies that our quantum memory cannot be mimicked by any classical device. We store a displaced entangled state of two sideband modes of light ˆ a + and ˆ a − with the frequencies ω ± = ω 0 ± ω L , where ω 0 is the carrier frequency of light. The entanglement condition for this Einstein–Podolsky–Rosen state 6 is Var( ˆ X + + ˆ X − ) + Var( ˆ P + − ˆ P − ) < 2 (ref. 30) where canonical quadrature operators obey [ ˆ X ± , ˆ P ± ]= i. For a vacuum state Var( ˆ X vac ) = Var( ˆ P vac ) = 1/2. The entanglement of the ˆ a + and ˆ a − modes is equivalent to simultaneous squeezing of the cos(ω L t ) mode ˆ x Lc = ( ˆ X + + ˆ X − )/ √ 2; ˆ p Lc = ( ˆ P + + ˆ P − )/ √ 2 and the corresponding sin(ω L t ) mode. Before the input state of light undergoes various losses it is a 6 dB squeezed state. In the photon-number representation for the two modes, the state is |〉= 0.8|0〉 + |0〉 − + 0.48|1〉 + |1〉 − + 0.29|2〉 + |2〉 − + 0.18|3〉 + |3〉 − + ···. The displaced squeezed states are produced (Fig. 1a) using an optical parametric amplifier 31 (OPA) with the bandwidth of 8.3 MHz and two electro-optical modulators (EOMs; see the Methods section for details). The alphabet of quantum states  i , which we refer to as ‘initial pure states’ (see the inset in Fig. 2 and Table 1) is generated by displacing the two-mode squeezed vacuum state by varying values [〈x L 〉; 〈p L 〉] = [0, 3.8, 7.6; 0, 3.8, 7.6] NATURE PHYSICS | VOL 7 | JANUARY 2011 | www.nature.com/naturephysics 13 © 2011 Macmillan Publishers Limited. All rights reserved.