Quantum systems have the potential to revolutionise present technology employing powerful quantum computers, unconditionally secure quantum cryptography, and extremely precise metrology. This project has focused on two aspects of how to use quantum systems for information processing. One aspect has been the distribution of a special kind of quantum correlations called entanglement, which is a key ingredient in protocols for secure networks and quantum enhanced sensors. By encoding information in physical systems with integrated error detection, we have shown that the performance of two-party communication can be greatly enhanced for limited experimental parameters. Another aspect of the project has been to investigate how the constituents of a quantum computer might be realised with current experimental platforms. To this end, we propose to combine heralded operations with a form of redundant encoding across many physical systems so that errors can not only be detected, but also corrected. This would allow for efficient quantum computation despite various experimental imperfections.

### Introduction

The technological advancements during the past decades have been tremendous. Computers have evolved from filling a factory hall to fit the size of a pocket in only half a century. However, as the components become smaller and smaller, curious effects not described by the classical Newtonian physics begin to emerge. In order to accurately describe these effects, which can be quite counter-intuitive, it is necessary to resort to quantum mechanics. The question is now what these quantum effects can be used for? In effort to answer this question a completely new branch of physics called quantum information theory (see Box 1) has emerged.

##### Quantum Information Theory

Studies how information can be encoded and manipulated in quantum systems.

Quantum systems are physical systems whose behaviour is described by quantum mechanics.

Information is encoded in quantum bits, which are the analogue of classical bits (0 and 1)

In this project, we have focused on two eminent questions in quantum information theory. One question is how to efficiently distribute entanglement (see Box 2) over long distances to be used for e.g. secure communication. The same sensitivity of the correlations that guarantees cryptographic security makes it very hard to create entanglement over long distances due to the detrimental effect of various noise sources and losses. By employing an integrated error detection system, which detects certain kinds of losses, we have shown how to greatly boost the rate of entanglement distribution even for limited experimental parameters. The other question is how to perform quantum computation in the presence of various experimental imperfections, which will introduce noise and limit the advantage of quantum computation over classical computation. To this end, we have investigated how error detection similar to what we have proposed for quantum communication can be combined with logical encodings to perform efficient quantum computation even in the presence of substantial losses.

##### Entanglement

Strong correlations between two or more quantum systems that have no classical counterpart.

Extracting information from entangled quantum systems leaves a trace in the correlations making it possible to detect any eavesdropper.

### Quantum Gate with Integrated Error-Detection

To process information, it is necessary to perform logical operations, so-called gates, on the information. Gates work on the bits (0’s and 1’s), which the information is encoded in. We have proposed how a quantum gate can be performed between two bits encoded in the internal energy states of two atoms trapped in a cavity (see Fig. 1).

The cavity can be thought of as two mirrors that trap light between them so that the light can interact strongly with the two atoms. A third atom in the cavity can be used both to control the cavity light and to detect whether any losses took place. The third atom is manipulated with a laser beam and can scatter light from the laser beam into the cavity. Through the interaction with the cavity light, a quantum gate is performed between the two ”bit” atoms. In reality, the system is not perfect and light can be scattered out of the cavity through various channels, which destroys the quantum information encoded in the bit atoms. However, by measuring the internal state of the third atom at the end of the gate, it can be determined whether this happened or not. As a result, the gate will not work every time, but when it works, we know that no information has been destroyed and hence, the heralded gate operation is almost perfect [1].

### Boosting Quantum Communication

The heralded quantum gate can be employed directly to boost the performance of entanglement distribution protocols called quantum repeaters (see Fig. 2). We have analysed a number of repeater schemes both with probabilistic and deterministic gates [2]. In particular, we found that the heralded gate described above significantly lowers the entanglement distribution time for limited experimental parameters even in comparison with the deterministic gates. The reason is that the quality of the entanglement can be much higher for the heralded gate, which is very important for cryptographic purposes [3]. The higher quality translates into a faster cryptographic communication than for the more noisy deterministic gates. Our results demonstrate that repeaters where error-detection is employed in the local operations are good candidates for practical entanglement distribution based on current experimental technology.

### Logical Encoding

We have also studied how error detection can be combined with a logical encoding in order to correct for failed gate attempts. The logical encoding will protect the quantum information even though the heralded gate fails and one can therefore simply retry the gate until successful. This corresponds to a deterministic quantum gate between two encoded bits with very small error due to the intrinsic error detection. We have found that a particular encoding known from quantum computation with light [4] can be combined with the atomic bits that we have considered for the heralded quantum gate. We are currently investigating how this combination can be used not only to make local gates, but also non-local gates between two bits that are far apart. This could be the basic building block for a quantum network similar to the Internet, but where quantum information is shared and distributed.

### Outlook

The overall goal of this project has been to help push the development of quantum technology further towards realisation in practical devices. Quantum technology has the potential to revolutionise our present technology. Quantum computers [5] can become important tools in anything from medicine to geoscience through their ability to model complex systems and handle Big Data. Secure communication can help protect whistle blowers or be an effective tool in the battle against terrorism. I therefore believe that it is highly relevant to further investigate and develop quantum technology as potentially it can have an impact on many of the challenges the world is facing in today.

#### About the Support from the Carlsberg Foundation, Johannes Borregaard says:

"This project was carried out with the support from the Carlsberg Foundation. The generous Carlsberg Foundation’s Internationalisation Fellowship made it possible for me to work in one of the most esteemed quantum optics and quantum information groups in the world at Harvard University. This has had a tremendous effect on the outcome of the project and opened up a variety of future research directions for me to pursue."

[1] J. Borregaard, P. Kómár, E. M. Kessler, A. S. Sørensen, and M. D. Lukin, Phys. Rev. Lett. 114, 110502 (2015).

[2] J. Borregaard, P. Kómár, E. M. Kessler, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 92, 012307 (2015).

[3] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).

[4] T. C. Ralph, A. J. F. Hayes, and A. Gilchrist, Phys. Rev. Lett. 95, 100501 (2005).

[5] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Nature 464, 45 (2010).