Entangled quantum particles have correlations stronger than those allowed by classical physics. These correlations are at the heart of deep foundational questions in quantum mechanics [1][2][3] , and form the basis of many emerging quantum technologies [4][5][6][7][8][9] . Although the discrete variables of up to 14 ions 10 and the continuous variables between three intense optical beams 11,12 have been entangled, it has remained an open challenge to entangle the continuous properties of three or more individual particles. Here we experimentally demonstrate genuine tripartite continuous-variable entanglement between three separated particles. In our set-up the three particles are photons created directly from a single input photon; the creation process leads to quantum correlations between the energies and emission times of the photons. The entanglement between our photons is the three-party generalization of the Einstein-Podolsky-Rosen 1 correlations for continuous variables, and could serve as a valuable resource in a wide variety of quantum information tasks.We directly generate three entangled photons using the nonlinear process of cascaded spontaneous parametric downconversion (C-SPDC; ref. 13). In downconversion, a pump photon, with frequency ω p , inside a nonlinear material will occasionally fission into a pair of daughter photons with frequencies ω 0 and ω 1 . The total energy in the process is conserved 14 withhω p =hω 0 +hω 1 . The daughter photons share strong energy and time correlations that are the hallmark of entanglement 15,16 . The SPDC process is repeated with one of these daughter photons, at ω 0 , now serving as the pump, creating a pair of granddaughter photons simultaneously at ω 2 and ω 3 . Again energy is conserved, and the total energy of the the three photons created in C-SPDC must sum to the energy of the pump:hω p =hω 1 +hω 2 +hω 3 . The simplified representation of our three-photon state in frequency space, assuming a monochromatic pump, has the form( 1) where G 1 (ω 1 , ω p − ω 1 ) and G 2 (ω 2 , ω p − ω 1 − ω 2 ) are the jointspectral functions resulting from the phase-matching conditions of the first and second SPDC crystals respectively 17 . The three photons, consequently, share strong spectral correlations and exhibit genuine tripartite energy-time entanglement.To verify the tripartite entanglement of the photons generated in our C-SPDC process we use continuous-variable entanglement criteria, which we derive based on the work in ref. A narrowband pump laser at 404 nm downconverts into a pair of orthogonally polarized photons at 842 and 776 nm inside a periodically-poled KTP crystal (PPKTP). A filter (FP) removes the remaining pump light. A polarizing beamsplitter (PBS) is used to separate the two photons, and narrowband filters, F0 and F1, are used to block stray light. The photon at 842 nm is coupled into a single-mode fibre (SMF) and sent to the single-photon detector D1. The photon at 776 nm is coupled into single-mode polarization maintaining fibre (PMF) and sent to a PP...
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Quantum correlations are critical to our understanding of nature, with far-reaching technological [1][2][3][4] and fundamental impact. These often manifest as violations of Bell's inequalities [5][6][7][8], bounds derived from the assumptions of locality and realism, concepts integral to classical physics. Many tests of Bell's inequalities have studied pairs of correlated particles; however, the immense interest in multi-particle quantum correlations is driving the experimental frontier to test systems beyond just pairs. All experimental violations of Bell's inequalities to date require supplementary assumptions, opening the results to one or more loopholes, the closing of which is one of the most important challenges in quantum science. Individual loopholes have been closed in experiments with pairs of particles [9][10][11][12][13][14] and a very recent result closed the detection loophole in a six ion experiment [15]. No experiment thus far has closed the locality loopholes with three or more particles. Here, we distribute three-photon Greenberger-Horne-Zeilinger entangled states[16] using optical fibre and free-space links to independent measurement stations. The measured correlations constitute a test of Mermin's inequality [17] while closing both the locality and related freedom-of-choice loopholes due to our experimental configuration and timing. We measured a Mermin parameter of 2.77 ± 0.08, violating the inequality bound of 2 by over 9 standard deviations, with minimum tolerances for the locality and freedom-of-choice loopholes of 264 ± 28 ns and 304 ± 25 ns, respectively. These results represent a significant advance towards definitive tests of the foundations of quantum mechanics[18] and practical multi-party quantum communications protocols [19].In his breakthrough work, John Bell[5] derived upper bounds on the strength of correlations exhibited by local hidden variable (LHV) theories, very general models of nature in which measurement outcomes in one region of space are independent of the events in other space-like separated regions. Quantum mechanical correlations can violate these bounds. Greenberger, Horne, and Zeilinger (GHZ) extended Bell's argument to the scenario with three-particle entangled states, and showed they could manifest violations of local realism in a fundamentally different way [16,20]. The GHZ argument was converted into the form of an inequality by Mermin[17] which we experimentally tested.An ideal Bell inequality experiment requires separating two or more particles by a large distance and making highefficiency local measurements on those particles using randomly chosen settings and comparing these results [21,22]. The first Bell inequality tests were carried out using twophoton cascades in atomic systems [7,8]. Mermin's inequality was violated using three-photon entanglement from a parametric down-conversion source [23]. However, these and the many other Bell experiments that followed are subject to one or more loopholes that could, in principle, be exploited to yield a violat...
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