Entanglement Swapping between Discrete and Continuous Variables

Abstract

We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is verified without post-selection by the logarithmic negativity of up to 0.28±0.01. Furthermore, our analysis shows that the optimally transferred state can be post-selected into a highly entangled state that violates a Clauser-Horne-Shimony-Holt inequality by more than 4 standard deviations, and thus it may serve as a resource for quantum teleportation and quantum cryptography.PACS numbers: 03.65. Ud, 03.67.Hk, 42.50Ex Quantum entanglement can be created between two distant quantum systems that have never directly interacted. This effect, called entanglement swapping [1][2][3][4][5][6][7][8], is a building block for quantum communication and computation [9][10][11][12]. It was originally proposed and demonstrated for discrete-variable (DV) optical systems [1][2][3][4]. The protocol starts with two entangled pairs, A-B and C-D, each represented either by twin photons or by a single photon split into two distinct modes [ Fig. 1 (a)].A joint projective measurement of B and C onto one of the four two-qubit Bell states then leads to an entangled state for A and D, even though A and D never directly interact with each other. Entanglement swapping can also be interpreted as the transfer of one half of an entangled state, either from B to D or from C to A, by quantum teleportation [13]. It is a key element for quantum networking [9], quantum computing [10], quantum cryptography [14], and especially long-distance quantum communication by means of quantum repeaters [11,12]. However, in this DV setting solely based upon single photons, due to the heralded conditional entangled-state generation and the probabilistic linear-optics Bell-state measurement (BSM), successful entanglement swapping events occur very rarely. As a result, in a quantum repeater for example, long-distance entangled-pair creation rates would be correspondingly low and requirements on the coherence times of the local quantum memories at each repeater station impractically high. In addition, the observation and verification of the final entanglement between A and D in the DV scheme typically requires postselection.Entanglement swapping was later extended to continuous-variable (CV) systems [15,16], where the pairs A-B and C-D each correspond to the two modes of a two-mode squeezed, quadrature-entangled state [5,6] [ Fig. 1(b)]. Since such entangled states are available on demand and a linear-optics BSM in the quadrature basis can be performed without failure, entanglement can be swapped deterministically and verified without postselection [7,8]. However, due to the finite squeezing of both initial entanglement sources, the final entanglement after swapping in the ...

Discorrelated Quantum States

“…In fact the statistics of discorrelation can be interpreted as a generalised HOM-type bosonic bunching effect for higher numbers of photons, or as a displacement of the HOM state | 〉 − | 〉 ( 2, 0 0, 2 ) 1 2 , which retains a similar quantum signature in the photon-number basis. Our procedure is bears a practical resemblance to generating discrete-continuous hybrid entanglement [59][60][61] , although here we map, rather than swap, discrete-variable path entanglement to continuous-variable entanglement.…”

Hybrid Rabi interactions with traveling states of light

“…For optical modes, decomposition can be typically done by first expressing an interaction as a sequence of ladder operatorsâ andˆ † a [4][5][6][7][8][9][10]. Recently, non-Gaussian quantum states and operations conditionally achieved by photon subtractions and additions have been proposed to achieve noiseless amplifier [11,12], entangle macroscopic states [13] to apply them in teleportation [14][15][16], remote state preparation [17] and quantum steering [18,19]. A conditional superposition of ladder operators can experimentally emulate nonlinearity for weak states of light [20].…”

“…Examples are quantum teleportation of a DV using CV protocol [14] or the teleportation of CV qubit to qubit [15], quantum repeater using hybrid protocol [76] or building on-chip integrated circuits [77]. Hybrid optical states have been generated experimentally to entangle the DV and CV [16][17][18][19][78][79][80][81][82][83][84]. Therefore, a natural question arises about whether and up to what extent we can induce the nonlinear effects of RI all-optically.…”

Hybrid photonic loss resilient entanglement swapping

“…These hybrid states of light are entangled discrete and CV quantum states. Hybrid states of light are particularly effective for ES schemes, and have been used in experimental proofs using squeezed states as the CV part [31] and also coherent states [32]. The DV part uses as basis states the vacuum and single photon Fock (number) states, and the CV part uses the basis states of nearly orthogonal coherent states.…”