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A fair gambling is hard to be made between two spatially separated parties without introducing a trusted third party. Here we propose a novel gambling protocol, which enables fair gambling between two distant parties without the help of a third party. By incorporating the key concepts and methods of game theory, our protocol will force the two parties to move their strategies to a Nash-equilibrium point which guarantees the fairness through the physical laws of quantum mechanics. Furthermore, we show that our protocol can be easily adapted to a biased version, which would find applications in lottery, casino, etc. A proof-of-principle optical demonstration of this protocol is reported as well.

A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). Furthermore, QPT is an essential method in determining how a process acts on quantum mechanical states. For example for quantum technology, QPT is used to characterise multi-qubit processors and quantum communication channels; across quantum physics QPT of some form is often the first experimental investigation of a new physical process, as shown in the recent research into coherent transport in biological mechanisms. However, the precision of QPT is limited by the fact that measurements with single-particle probes are subject to unavoidable shot noise---this holds for both single photon and laser probes. In situations where measurement resources are limited, for example, where the process is rapidly changing or the time bandwidth is constrained, it becomes essential to overcome this precision limit. Here we devise and demonstrate a scheme for tomography which exploits non-classical input states and quantum interferences; unlike previous QPT methods our scheme capitalises upon the possibility to use simultaneously multiple photons per mode. The efficiency---quantified by precision per photon used---scales with larger photon number input states. Our demonstration uses four-photon states and our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods---in the ideal case one four-photon probe state yields the same amount of statistical information as twelve single probe photons.

Quantum metrology research promises approaches to build new sensors that achieve the ultimate level of precision measurement and perform fundamentally better than modern sensors. Practical schemes that tolerate realistic fabrication imperfections and environmental noise are required in order to realise quantum-enhanced sensors and to enable their real-world application. We have demonstrated the key enabling principles of a practical, loss-tolerant approach to photonic quantum metrology designed to harness all multi-photon components in spontaneous parametric downconversion---a method for generating multiple photons that we show requires no further fundamental state engineering for use in practical quantum metrology. We observe a quantum advantage of 28% in precision measurement of optical phase using the four-photon detection component of this scheme, despite 83% system loss. This opens the way to new quantum sensors based on current quantum-optical capabilities., Comment: 8 pages, 7 figures, 2 tables

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm can efficiently find the eigenvalue of a given eigenvector but requires fully coherent evolution. We present an alternative approach that greatly reduces the requirements for coherent evolution and we combine this method with a new approach to state preparation based on ans\"atze and classical optimization. We have implemented the algorithm by combining a small-scale photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry: calculating the ground state molecular energy for He-H+, to within chemical accuracy. The proposed approach, by drastically reducing the coherence time requirements, enhances the potential of the quantum resources available today and in the near future.

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures., Comment: 7 pages, 3 figures

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations.

Quantum walks of correlated particles offer the possibility to study large-scale quantum interference, simulate biological, chemical and physical systems, and a route to universal quantum computation. Here we demonstrate quantum walks of two identical photons in an array of 21 continuously evanescently-coupled waveguides in a SiOxNy chip. We observe quantum correlations, violating a classical limit by 76 standard deviations, and find that they depend critically on the input state of the quantum walk. These results open the way to a powerful approach to quantum walks using correlated particles to encode information in an exponentially larger state space.

While quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations-a requirement in many quantum algorithms, simulations and metrology. The technique is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. We demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity., Comment: 9 pages, 8 figures

A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and in the one-way quantum computer model, the smallest non-trivial quantum codes to tackle this problem. In the experiment, we encode single-qubit input states into highly-entangled multiparticle codewords, and we test their ability to protect encoded quantum information from detected one-qubit loss error. Our results prove the in-principle feasibility of overcoming the qubit loss error by quantum codes., Comment: "Quantum Computing even when Photons Go AWOL". published version

Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A phase shift of $\pi$ related to the anyon braiding is observed, confirming the prediction of the fractional statistics of Abelian 1/2-anyons., Comment: revised version 3, revTex, 4.3 pages, 4 figures, notes and reference added

We present a feasible and efficient scheme, and its proof-of-principle demonstration, of creating entangled photon pairs in an event-ready way using only simple linear optical elements and single photons. The quality of entangled photon pair produced in our experiment is confirmed by a strict violation of Bell's inequality. This scheme and the associated experimental techniques present an important step toward linear optics quantum computation., Comment: 4 pages, 4 figures

Graph states are special kinds of multipartite entangled states that correspond to mathematical graphs where the vertices take the role of quantum spin systems and the edges represent interactions. They not only provide an efficient model to study multiparticle entanglement, but also find wide applications in quantum error correction, multi-party quantum communication and most prominently, serve as the central resource in one-way quantum computation. Here we report the creation of two special instances of graph states, the six-photon Greenberger-Horne-Zeilinger states -- the largest photonic Schr\"{o}dinger cat, and the six-photon cluster states-- a state-of-the-art one-way quantum computer. Flexibly, slight modifications of our method allow creation of many other graph states. Thus we have demonstrated the ability of entangling six photons and engineering multiqubit graph states, and created a test-bed for investigations of one-way quantum computation and studies of multiparticle entanglement as well as foundational issues such as nonlocality and decoherence.

The maximum distance of quantum communication is limited due to the photon loss and detector noise. Exploiting entanglement swapping, quantum relay could offer ways to extend the achievable distance by increasing the signal to noise ratio. In this letter we present an experimental simulation of long distance quantum communication, in which the superiority of quantum relay is demonstrated. Assisted by quantum relay, we greatly extend the distance limit of unconditional secure quantum communication., Comment: 12 pages (with appendix), 3 figures, submitted

We report an experimental realization of bit-flip error rejection for error-free transfer of quantum information through a noisy quantum channel. In the experiment, an unknown state to be transmitted is encoded into a two-photon entangled state, which is then sent through an engineered noisy quantum channel. At the final stage, the unknown state is decoded by a quantum parity measurement, successfully rejecting the erroneous transmission over the noisy quantum channel., Comment: 4 pages, 3 figures

Quantum secret sharing (QSS) is a protocol to split a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. In the scheme, three parties Alice, Bob and Charlie first share a three-photon entangled state, Charlie can then force Alice and Bob to cooperate to be able to establish the secret key with him by performing proper polarization measurements on his photon and announcing which polarization basis he has chosen. In a similar manner, in third-man quantum cryptography (TQC) the third-man, Charlie, can control whether Alice and Bob can communicate in a secure way while he has no access whatsoever on the content of the communication between Alice and Bob. Although QSS and TQC are essential for advanced quantum communication, the low intensity multi-photon entanglement source has made their realization an extreme experimental challenge. Here, exploiting a high intensity four-photon entanglement source we report an experimental realization of QSS and TQC . In the experiment, a key of low quantum bit error rate (QBER) 0.35% is obtained using a simple error reduction scheme., Comment: 4 pages, 3 figures, submitted

Cluster states serve as the central physical resource for the measurement-based quantum computation. We here present a simple experimental demonstration of the scalable cluster-state-construction scheme proposed by Browne and Rudolph. In our experiment, three-photon cluster states are created from two Bell states using linear optical devices. By observing a violation of three-particle Mermin inequality of $|< \textit{A}>| = 3.10\pm0.03 $, we also for the first time report a genuine three-photon entanglement. In addition, the entanglement properties of the cluster states are examined under $\sigma_z$ and $\sigma_x$ measurements on a qubit., Comment: 4 pages, 4 figures, submitted

We report an experimental realization of both optimal asymmetric cloning and telecloning of single photons by making use of partial teleportation of an unknown state. In the experiment, we demonstrate that, conditioned on the success of partial teleportation of single photons, not only the optimal asymmetric cloning can be accomplished, but also one of two outputs can be transfered to a distant location, realizing the telecloning. The experimental results represent a novel way to achieve the quantum cloning and may have potential applications in the context of quantum communication., Comment: 4 pages and 4 figures