An experimental implementation of oblivious transfer in the noisy storage model.

Cryptography's importance in our everyday lives continues to grow in our increasingly digital world. Oblivious transfer has long been a fundamental and important cryptographic primitive, as it is known that general two-party cryptographic tasks can be built from this basic building block. Here we show the experimental implementation of a 1-2 random oblivious transfer protocol by performing measurements on polarization-entangled photon pairs in a modified entangled quantum key distribution system, followed by all of the necessary classical postprocessing including one-way error correction. We successfully exchange a 1,366 bit random oblivious transfer string in ~3 min and include a full security analysis under the noisy storage model, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of using today's quantum technologies to implement secure two-party protocols.

Quantum computers.

Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.

Geometric phase with nonunitary evolution in the presence of a quantum critical bath.

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quantum geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment--leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-half coupled to an environment. In particular we are interested in baths near a quantum phase transition, which are known to induce strong decoherence. The experiments are done with a NMR quantum simulator, where we emulate qualitatively the influence of a critical environment using a simple one-qubit model.

Experimental approximation of the Jones polynomial with one quantum bit.

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

Entangled quantum key distribution over two free-space optical links.

We report on the first real-time implementation of a quantum key distribution (QKD) system using entangled photon pairs that are sent over two free-space optical telescope links. The entangled photon pairs are produced with a type-II spontaneous parametric down-conversion source placed in a central, potentially untrusted, location. The two free-space links cover a distance of 435 m and 1,325 m respectively, producing a total separation of 1,575 m. The system relies on passive polarization analysis units, GPS timing receivers for synchronization, and custom written software to perform the complete QKD protocol including error correction and privacy amplification. Over 6.5 hours during the night, we observed an average raw key generation rate of 565 bits/s, an average quantum bit error rate (QBER) of 4.92%, and an average secure key generation rate of 85 bits/s.

Spin based heat engine: demonstration of multiple rounds of algorithmic cooling.

We experimentally demonstrate multiple rounds of heat-bath algorithmic cooling in a 3 qubit solid-state nuclear magnetic resonance quantum information processor. By pumping entropy into a heat bath, we are able to surpass the closed system limit of the Shannon bound and purify a single qubit to 1.69 times the heat-bath polarization. The algorithm combines both high fidelity coherent control and a deliberate interaction with the environment. Given this level of quantum control in systems with larger reset polarizations, nearly pure qubits should be achievable.

Experimental quantum communication without a shared reference frame.

We present an experimental realization of a robust quantum communication scheme [Phys. Rev. Lett. 93, 220501 (2004)] using pairs of photons entangled in polarization and time. Our method overcomes errors due to collective rotation of the polarization modes (e.g., birefringence in optical fiber or misalignment), is insensitive to the phase's fluctuation of the interferometer, and does not require any shared reference frame including time reference, except the need to label different photons. The practical robustness of the scheme is further shown by implementing a variation of the Bennett-Brassard 1984 quantum key distribution protocol over 1 km optical fiber.

Benchmarking quantum control methods on a 12-qubit system.

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.

Characterization of complex quantum dynamics with a scalable NMR information processor.

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance.

The counter-intuitive properties of quantum mechanics have the potential to revolutionize information processing by enabling the development of efficient algorithms with no known classical counterparts. Harnessing this power requires the development of a set of building blocks, one of which is a method to initialize the set of quantum bits (qubits) to a known state. Additionally, fresh ancillary qubits must be available during the course of computation to achieve fault tolerance. In any physical system used to implement quantum computation, one must therefore be able to selectively and dynamically remove entropy from the part of the system that is to be mapped to qubits. One such method is an 'open-system' cooling protocol in which a subset of qubits can be brought into contact with an external system of large heat capacity. Theoretical efforts have led to an implementation-independent cooling procedure, namely heat-bath algorithmic cooling. These efforts have culminated with the proposal of an optimal algorithm, the partner-pairing algorithm, which was used to compute the physical limits of heat-bath algorithmic cooling. Here we report the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance of a solid-state ensemble three-qubit system. We demonstrate the repeated repolarization of a particular qubit to an effective spin-bath temperature, and alternating logical operations within the three-qubit subspace to ultimately cool a second qubit below this temperature. Demonstration of the control necessary for these operations represents an important step forward in the manipulation of solid-state nuclear magnetic resonance qubits.

Unconditional security of a three state quantum key distribution protocol.

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.

Robust quantum communication using a polarization-entangled photon pair.

Noise and imperfection of realistic devices are major obstacles for implementing quantum cryptography. In particular, birefringence in optical fibers leads to decoherence of qubits encoded in photon polarization. We show how to overcome this problem by doing single qubit quantum communication without a shared spatial reference frame and precise timing. Quantum information will be encoded in pairs of photons using tag operations, which corresponds to the time delay of one of the polarization modes. This method is robust against the phase instability of the interferometers despite the use of time bins. Moreover synchronized clocks are not required in the ideal no photon loss case as they are necessary only to label the different encoded qubits.

Robust polarization-based quantum key distribution over a collective-noise channel.

We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting to interferometry or two-way quantum communication, thereby circumventing, respectively, the need for high precision timing and the threat of Trojan horse attacks.

Experimental realization of noiseless subsystems for quantum information processing.

We demonstrate the protection of one bit of quantum information against all collective noise in three nuclear spins. Because no subspace of states offers this protection, the quantum bit was encoded in a proper noiseless subsystem. We therefore realize a general and efficient method for protecting quantum information. Robustness was verified for a full set of noise operators that do not distinguish the spins. Verification relied on the most complete exploration of engineered decoherence to date. The achieved fidelities show improved information storage for a large, noncommutative set of errors.

Benchmarking quantum computers: the five-qubit error correcting code.

The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding, and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.

A scheme for efficient quantum computation with linear optics.

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Theory of quantum error correction for general noise

A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.

An algorithmic benchmark for quantum information processing

Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms and for secure communication. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.