Distribution of Entanglement with Unentangled Photons
Authors: Margherita Zuppardo1, Alessandro Fedrizzi2, Tomasz Paterek1,3
1School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
2Centre for Engineered Quantum Systems and Centre for Quantum Computer and Communication Technology, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
3Centre for Quantum Technologies, National University of Singapore, Singapore.
Many possible applications of quantum mechanics, in particular in communication, make use of entanglement between two or more systems. This is because entangled particles can be more strongly correlated than any correlations allowed in classical physics. Not all entangled couples share the same amount of entanglement: entanglement can be quantified, and the larger the amount of shared entanglement, the more secure and accurate the communication can be.
This is why, in view of experiments or communication technologies involving quantum mechanics, finding new and better protocols that allow cheap and effective ways to create entanglement at a distance is an important goal. A conceptually simple way of doing this would be creating entanglement between two particles, A and B, by making them interact in the same place. For instance, if the particles are photons, it is possible that they will share entanglement by going through a quantum gate. After that, Alice will send the photon B to where Bob is and, if the experiment is done properly, A and B will be sharing entanglement over distance. We call this a "direct" protocol.
However, this is not the only, or always the best way to distribute entanglement. For example, we can define a class of "indirect" protocols, that would work as Fig. 1 shows. Particles A and B are originally far apart, but Alice possesses a third particle, C, in her lab. Particles A and C interact locally, then C is sent to Bob, who makes it interact with B. Again, all this process can in the end create entanglement between particles A and B. Indirect protocols have an unusual property : they can work even if C stays unentangled (separable) from the other particles. This fact highlights a phenomenon unique to quantum mechanics: there exist measurable and useful physical quantities, such as entanglement, that can be transmitted either with or without being carried! However, indirect protocols cannot work if the particles are uncorrelated. They need to share a weaker form of quantum correlation, called quantum discord [2,3] and this is, in fact, one of the few applications of quantum discord that are known today.
Fig. 1: Indirect protocols for entanglement distribution. Alice locally makes her system A interact with the carrier system C, which is then sent to Bob's site. We call such protocols “indirect” because it is possible to establish entanglement between the respective laboratories even though there was no initial entanglement between them and no entanglement is communicated. This is accomplished as follows: In step (1), the fully separable initial state of the three systems is prepared, in our protocol a Bell diagonal state mixed with white noise for A and B, that are completely uncorrelated with C. In step (2) Alice applies a C-phase gate on A and C, which keeps the latter separable from the rest of the systems but creates entanglement between A and joint system made out of B and C together. In step (3), the unentangled carrier C is transmitted to Bob. As shown in panel (4), this establishes entanglement between the laboratories of Alice and Bob.
We realized  one of the first experiments [5,6] in which entanglement is created by using an unentangled carrier, with photonics qubits. Our goal was to show that such protocols are feasible with state of the art laboratory technology and that such protocols are practically relevant if communication and storage of qubits suffers from noise. In the experiment we generate two pairs of photons using a nonlinear crystal. We name three photons A, B and C. The fourth photon is used as a trigger, to check the success of photon generation.
Fig 2: Experimental setup. (a) Equivalent quantum circuit diagram for our protocol. (b) Two pairs of single photons are created via spontaneous parametric downconversion in a β-barium borate crystal (BBO) pumped by a frequency-doubled femtosecond Ti:Sapphire laser at 820nm. One photon serves as a trigger, while the other three are initialised with polarising beamsplitters (PBS), half-wave (HWP) and quarter-wave plates (QWP). The photons representing systems A and C are subjected to a probabilistic controlled-phase gate based on two-photon interference at a partially polarising beamsplitter (PPBS). Projective measurements are made with a combination of HWP, QWP and PBS, and detected by single-photon avalanche photodiodes (APD) connected to a coincidence logic.
Fig. 2 shows the setup of the experimental apparatus. Following the recipe of reference , particles A and B are generated in a separable state in the polarization degrees of freedom. The interaction between A and C is determined by a gate called controlled-phase gate, or C-phase gate. After this gate, particle C is sent to Bob. In Fig. 3 we show that A shares some entanglement with the subsystem made of B and C, after C is sent to Bob. This is revealed by a negative number in the plot (so called negativity). Finally, we have shown that the final state is not entangled between C and the remaining two particles and that the initial state is completely separable. All this shows that, in our experiment, entanglement is created without being carried.
Fig. 3: Determining entanglement properties after the distribution. We reconstructed the quantum state at the end of the protocol and calculated from it entanglement measure called negativity. The state is entangled if the plot shows negative number, i.e. in the partition A|BC (red dot and bar), and reveals the success of the distribution of entanglement. At the same time, there is no negativity in the other two partitions, C|AB (blue dot and bar) and B|AC (marked in brown). This means that the system could be separable in such partitions, that, however, needs to be additionally proven. We proved it by finding explicit separable decompositions of the state. All this shows that our protocol indeed uses a separable carrier.
One application of such protocols makes use of their robustness to noise. This is a very important problem because, in nature, noise is always created by the interaction with the environment and quantum correlations can be easily destroyed by it. In a laboratory, this problem can be partially avoided, but protocols that can work in the presence of noise can be much cheaper, and so have a large technological potential. We modeled noise as a dephasing and a depolarizing quantum channel, whose noise parameters are labeled with δ, and added the possibility that local noise in the places where the photons are generated precludes the creation of pure states, labeling the mixedness of initial state by p. As Fig. 4 shows, for a wide range of the channel noise parameters, entanglement is achieved for a higher level of mixedness (the blue regions), when using a separable carrier.
Fig. 4: Robustness to noise of direct and indirect distribution. In the direct protocol Alice prepares an entangled state in her lab and sends particle B to Bob. Due to the noise in the channel not all the entanglement will survive. In the indirect protocol Alice and Bob start with this state and a third particle, C, interacts with A via a C-phase gate, and is then sent to Bob. In this way it is taken into account that in order to complete the indirect protocol one has to first prepare the initial state between the labs of Alice and Bob. Panels a) and b) present results for different types of noise. In the pink area, the direct distribution creates some entanglement. Within the blue area, entanglement grows by sending a separable carrier. In the regions with only blue color, sending an unentangled particle is the only effective way of creating entanglement.
In conclusion, distributing entanglement via separable states is a counterintuitive and effective technique, already experimentally available, with future applications in communication technology, as a means to counteract noise when creating quantum entanglement at a distance.
 T.S. Cubitt, F. Verstraete, W. Dür, J.I. Cirac. "Separable States can be used to distribute entanglement". Physical Review Letters, 91, 037902 (2003). Abstract.
 L. Henderson, V. Vedral. "Classical, quantum and total correlations". Journal of Physics A, 34, 6899 (2001). Abstract.
 Harold Ollivier and Wojciech H. Zurek. "Quantum discord: a measure of the quantumness of correlations". Physical Review Letters, 88, 017901 (2001). Abstract.
 A. Fedrizzi, M. Zuppardo, G. G. Gillett, M. A. Broome, M. P. Almeida, M. Paternostro, A. G. White, T. Paterek. "Experimental distribution of entanglement with separable carriers". Physical Review Letters, 111, 230504 (2013). Abstract.
 Christian Peuntinger, Vanessa Chille, Ladislav Mišta, Jr., Natalia Korolkova, Michael Förtsch, Jan Korger, Christoph Marquardt, Gerd Leuchs. "Distributing Entanglement with Separable States". Physical Review Letters, 111, 230506 (2013). Abstract.
 Christina E. Vollmer, Daniela Schulze, Tobias Eberle, Vitus Händchen, Jaromír Fiurášek, Roman Schnabel. "Experimental Entanglement Distribution by Separable States". Physical Review Letters, 111, 230505 (2013). Abstract.
 Alastair Kay. "Using Separable Bell-Diagonal States to Distribute Entanglement". Physical Review Letters, 109, 080503 (2012). Abstract.