2006 Talk Abstracts
Session #1 Optical Quantum Computing and Networking
Terry Rudolf, Imperial College, London
Abstract: The primary technological hurdle facing linear optical quantum computation is commonly thought to be the construction of efficient sources and detectors. I will argue that the primary hurdle is in fact theoreticians who haven't devoted enough time to thinking about whether we can get by with the devices we have. In defense of this thesis I will discuss how, by making use of some neat features of cluster state computation, we can get by with much more noisy devices than one might have hoped, and why I am optimistic that smarter theoreticians then me should be able to relax these fault tolerant thresholds even further.
James Chin-Wen Chou, California Institute of Technology
Abstract: A critical requirement for diverse applications in Quantum Information Science is the capability to disseminate quantum resources over complex quantum networks. This requires the realization of a quantum memory that would allow the storage and retrieval of quantum states. Recently, atomic ensembles rise to be a promising candidate for this task. In this contribution we report observation of entanglement between two atomic ensembles located on different tables in distinct apparatuses separated by 2.8 meters. Quantum interference in the detection of a photon emitted by the samples projects the otherwise independent ensembles into an entangled state with one joint excitation stored remotely in 101'5atoms at each site. After a delay of 1 microsecond to demonstrate quantum memory, we confirm entanglement by mapping the state of the atoms to optical fields and then measuring mutual coherence and photon statistics for these fields. We thereby determine a quantitative lower bound for the entanglement of the joint state of the ensembles.
Thaddeus Ladd, Stanford University
Abstract: Long-distance (1000 km) quantum communication will require a quantum repeater system. For most existing repeater proposals, reasonable qubit-communication rates require technologies which are currently impractical, such as balanced, stabilized interferometry over very long distances or large numbers of efficient single-photon sources and detectors. We present detailed theoretical calculations demonstrating the feasibility of a more practical quantum repeater employing intense coherent light interacting dispersively with single emitters (atoms, quantum dots, semiconductor impurities, etc.). For a sufficient interaction strength, each emitter must be located in a high-Q optical cavity, but the weak-coupling regime is sufficient. Distribution of the intense coherent light among the intermediate qubits of the quantum channel followed by homodyne detection of the optical phase generates noisy, post-selected entangled pairs with high success probability. Local operations used for entanglement purification and entanglement swapping are based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Assuming small local optical loss and high-fidelity single-qubit rotations, these local operations may be completely deterministic. Simulations of this system show qubit-communication rates approaching 100 Hz and final fidelities above 99% for reasonable system parameters.
Danna Rosenberg, Los Alamos National Laboratory
Abstract. Under ideal conditions, quantum key distribution (QKD) provides a method for two users to communicate with security guaranteed by the laws of physics. In the real world, the security of such a system is closely tied to the properties of the source and the detectors. In particular, the detection efficiency and the dark-count rate of the detectors used at the receiver play a critical role in determining the maximum length of a secure link. Unlike standard avalanche photo-diodes, which typically have low efficiency and high dark-count rates at the telecommunication wavelengths, transition-edge sensors (TESs) have virtually no dark counts and can be engineered to have high efficiency at telecommunications wavelengths. By incorporating TESs into a QKD system, we were able to 1) transmit key across 202 km of dark optical fiber and 2) demonstrate key transmission secure against photon-number-splitting attacks over 100 km of dark fiber, setting two new records for fiber quantum key distribution.
Session #2: Quantum Measurement and Metrology
Hans Briegel, University of Innsbruck
Abstract: This talk will give an introduction to the theory of graph states. Graph states arise naturally in the context of the one-way quantum computer, but they play a significant role in other fields of quantum information, too. We will discuss various properties of graph states, including their generalizations and applications.
Michale Di Rosa, Los Alamos National Laboratory
Abstract. We propose to build a quantum nondemolition (QND) detector of single photons from the giant Kerr nonlinearity theoretically identified by Schmidt and Imamoglu . To our knowledge, the experimental work would represent the first single photon QND measurement by a cross-Kerr interaction, and we believe it would mark an important transition for the use of QND measurements in optics-based quantum computing. While single-photon QND measurements have been demonstrated through cavity QED, our use of a material nonlinearity will provide a QND measurement that can count photon numbers greater than one and allow photons to pass unimpeded for re-use in computations. We will review the theoretical template for the enhanced cross-Kerr interaction and show its match to an atomic system we have chosen for the experiments.  H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
Ognyan Oreshkov, University of Southern California
Abstract. We have shown that every generalized quantum measurement can be implemented as a sequence of weak measurements, and presented an explicit construction of these weak measurements. The measurement procedure has the structure of a random walk in state space, with the measurement ending when one of the end points is reached. This allows us to think of measurements in quantum mechanics as resulting from continuous stochastic evolutions, and to make use of the powerful tools of differential calculus in the study of the transformations that a system undergoes upon measurement. We have used this result to derive necessary and sufficient differential conditions for a function of the state to be an entanglement monotone, by looking at the behavior of a prospective monotone under infinitesimal local operations. As an application, we have used the differential conditions to construct a new entanglement monotone for three-qubit pure states, which depends on the sixth-order polynomial invariant identified by Kempe. Future projects include application of the measurement decomposition to quantum control, and searching for new classes of entanglement monotones.
Diego Dalvit (Los Alamos National Laboratory)
Abstract: We show how sub-Planck phase-space structures can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent states, are show to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. Implementations of this strategy in cavity QED and ion traps are described.
Session #3: Qubits In Condensed Matter
Eva Weig, University of California Santa Barbara
Abstract: Superconducting quantum bits are considered promising candidates for constructing a solid-state quantum computer. They are based on the Josephson junction, formed by sandwiching a thin dielectric between two superconducting leads, through which Cooper pairs can tunnel. The Josephson junction provides a nearly dissipationless, highly nonlinear circuit element that allows the construction of a quantum bit. A particular implementation, the phase qubit, is realized by current-biasing a Josephson junction near the critical current of the junction. Besides demonstrating long coherence times, phase qubits can be tuned over a large frequency range. Furthermore, they provide all the advantages of solid-state electrical circuits, as they can be fabricated using fully scalable conventional integrated circuit technology. In addition, controlled coupling to other quantum circuits can be achieved, facilitating readout and gate implementation. In order to achieve the maximum coherence time, to allow for multiple, complex quantum operations, the dissipation induced by the environment has to be minimized. Our research has therefore focused in part on minimizing environment-induced decoherence, and we have recently achieved a significant and important breakthrough, due to the realization that losses in the dielectrics, both in the Josephson junction itself and in associated circuitry, dominate the overall loss and limit the coherence time. Our demonstration of high visibility, long decoherence time qubits has been achieved by carefully redesigning and engineering our qubit circuit and the materials employed. Recent experiments have demonstrated qubit state preparation, manipulation and probing with a measurement fidelity of 95%. Rabi oscillations with a relaxation time Tl of 500 ns have been observed. Ramsey fringe as well as spin echo measurements yield decoherence times of T2 = 2 Tl and T2*= 150 ns. We have also begun to develop full quantum tomography of the qubit state. This experimental technique allows the reconstruction of the density matrix from a complete set of observables measured on an ensemble of identically prepared copies of the system. The detailed understanding of a single qubit will enable us to start focusing on coupled qubit systems. Experiments to violate Bells inequality as well as the implementation of a CNOT gate in a coupled qubit are in progress.
Wang Yao, Ren-Bao Liu and L. J. Sham (University of California San Diego)
Abstract. Department of Physics, University of California, San Diego Abstract: Electron spins in semiconductor quantum dots are natural carriers of qubit for quantum information processing. A major issue that has to be addressed is the spin decoherence. Consensus holds that at low temperature, the lattice nuclear spin is the dominant agent for decoherence. In this talk, I will present a quantum theory to the electron spin decoherence by a nuclear pair-correlation method for the electron- nuclear spin dynamics under a strong magnetic field and low temperature. The theory incorporates the electron nuclear hyperfine interaction, the intrinsic nuclear interactions, and the nuclear coupling mediated by the hyperfine interaction with the electron in question. Results for both single electron spin free-induction decay (FID) and ensemble electron spin echo will be discussed. Single spin FID is affected by both the intrinsic and the hyperfine-mediated nuclear interactions, with the dominance determined by the dot size and external field. The spin echo eliminates the hyperfine-mediated decoherence but only reduces the decoherence by the intrinsic nuclear interactions. Thus, the decoherence times for FID and spin echo are significantly different. Electron spin decoherence is explained in terms of the quantum entanglement: due to the hyperfine interaction, the nuclear spins in a quantum dot, driven by nuclear spin pair-wise flip-flops, evolve in different pathways in the Hilbert space for different electron spin states, resulting in the electron-nuclei entanglement and hence the electron spin decoherence. When the electron spin is flipped by a pulse, the nuclear spin states for different electron spin states swap their ·pathways, and could intersect in the Hilbert space, which disentangles the electron and the nuclei and hence restores the electron spin coherence. The coherence restoration by disentanglement and the conventional spin echo in ensemble dynamics are fundamentally different and generally occur at different time. Pulse sequences can be applied to force the disentanglement to coincide with the spin echo, making the coherence recovery observable in ensemble dynamics.
* This work was supported by NSF DMR- 0403465, NSAIARO, and DARPAIAFOSR.
Frank Verstraete, California Institute of Technology
Abstract. Entanglement theory provides a unique perspective on the properties of strongly correlated quantum systems. We will discuss numerical renormalization group methods on the one hand, and properties like topological quantum order in toric code states on the other hand.
Session #4: Quantum Algorithms
Cristopher Moore, University of New Mexico I Santa Fe Institute
Abstract: Ever since Shor's celebrated factoring algorithm, we have been looking for additional quantum algorithms that solve computer science problems exponentially faster than their classical counterparts. Most such algorithms fall under the general heading of the Hidden Subgroup Problem, in which we try to find the symmetries (e.g. periodicities) of some function defined on a group by measuring in the Fourier basis. When the function is defined on a non-Abelian group such as the permutation group, however (which is the group relevant to the Graph Isomorphism problem) the "frequencies" of a function become matrix valued representations. I will give an accessible introduction to the representation theory of finite groups, and explain why the non-Abelian Hidden Subgroup Problem remains a challenging and exciting frontier for quantum algorithms.
Dave Bacon, University of Washington
Abstract: Quantum computers can efficiently solve the hidden subgroup problem over abelian groups. This fact lies at the heart of Peter Shor's efficient quantum algorithm for factoring whole numbers. Whether quantum computers can efficiently solve the hidden subgroup problem over nonabelian groups is one of the grand outstanding challenges in the theory of quantum algorithms. Such efficiently algorithms would lead to efficient quantum algorithms for the graph isomorphism problem and for certain shortest vector in a lattice problems. Recently a tremendous amount of progress has been made on understanding the nonabelian hidden subgroup problem. In this talk I will discuss how some of this work has lead to efficient new quantum algorithms and in particular to such algorithms which move beyond the quantum fourier transform barrier. This is joint work with Andrew Childs (Caltech) and Wim van Dam (UCSB).
Andrew Landahl, University of New Mexico
Abstract: I will show that a class of "symmetry invariant" quantum query algorithms for searching an ordered list of N items can be expressed as a set of feasible solutions to a certain semidefinite program (SDP). By numerically solving this SDP, we have found quantum query algorithms for this problem that are more than twice as fast as the best possible classical algorithm. I will further demonstrate that symmetry invariance can be used to derive Grover's algorithm as an essentially unique solution for the unordered search problem. I will conclude with a discussion of the role of automated computer searches in the quest for finding new quantum algorithms.
Jonathan Walgate, University of Calgary
Abstract: A swashbuckling tale of greed, deception, and quantum data hiding on the high seas. When we hide or encrypt information, it's probably because that information is valuable. I present a novel approach to quantum data hiding based on this assumption. An entangled treasure map marks the spot where a hoard of doubloons is buried, but the sailors sharing this map want all the treasure for themselves! How should they study their map using local operations and classical communication? This simple scenario yields a surprisingly rich and counterintuitive game theoretic structure. A maximally entangled map performs no better than a separable one, leaving the treasure completely exposed. But non-maximally entangled maps can hide the information almost perfectly! Quantum data hiding was developed with two motivations. It is worth investigating purely as cryptographic scheme, allowing data to be concealed from cryptanalysts sharing a perfect copy. However it also provides an operational framework for studying entanglement and nonlocality, as it hinges on the difference between local and global physical information.
'Quantum buried treasure' schemes have four key advantages. Firstly, the local perspectives of those sharing the quantum system are clearly revealed, and this allows a more detailed comparison between the local and global information. (Previous schemes have treated local observers as a single collective eavesdropper, albeit operating under local constraints.) Secondly, interesting competitive situations emerge among the local parties. These suggest a useful role for game theory in quantum mechanics that emerges naturally from its nonlocal structure, unlike artificial attempts to unify the two. Thirdly, buried treasure provides a more realistic model both of encrypted information, which tends to be actually valuable, and of the motivations of those attempting the decryption. Last but not least, Alice and Bob get to be pirates!
Anthony Dutoi, University of California Berkeley
Abstract: The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer, but polynomially using quantum algorithms. We will discuss how such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the H20 and LiH molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the read-out register from approximately twenty to four. Different mappings of the molecular wave function to the quantum bits are discussed. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for stretched H2. The prospects of an experimental implementation of the algorithm, as well as precision considerations will be discussed. Our future and present research directions will be presented! . We will describe the main capabilities of our quantum simulation computer program (Tequila). Reference: A. Aspuru-Guzik, A. D. Dutoi, P. J Love, M Head-Gordon, Science 309 1704 (2005)
Session #5: Quantum Information Science with Atoms and Ions
Thad Walker, University of Wisconsin, Madison
Abstract: I will describe an apparatus designed to trap 1-50 Rb atoms in multiple dipole traps at spacings of 8 microns for a variety of quantum manipulation experiments. We have demonstrated site-addressable Rabi flopping at MHz rates with cross-talk of less than 0.001 to the neighboring site. The measured dephasing time of 870 microseconds gives a very good figure of merit for precision manipulation of the atoms confined in the traps. We have demonstrated high fidelity single-atom detection using a modulated readout scheme that avoids excited-state hyperfine mixing and heating due to the intense trap light. We have also observed sub-Poissonian atomic number distributions in the traps. The next step in these experiments involves excitation of the atoms to n 50 Rydberg states. In order to produce entanglement between atoms in neighboring sites, it will be advantageous to produce the Rydberg atoms under conditions where the Rydberg Rydberg interactions are strong (1/R/\3) and isotropic. I will describe how dressing the atoms with microwave fields allows such interactions.
Poul Jessen, University of Arizona
Abstract: Neutral atoms trapped in optical lattices provide an excellent platform for quantum information science, in part due to the very long lifetime of ground state populations and coherences, and in part due to the large experimental toolbox available to prepare, manipulate and measure their quantum state. I will describe experimental progress towards the demonstration of two-qubit quantum logic via controlled ground state collisions. These collisions, along with their ability to entangle atom pairs, can be probed in ensemble experiments where the collisional interaction is inserted between the pulses of a standard Ramsey interrogation sequence. An essential part of such an experiment is the ability to perform very high fidelity single qubit rotations. We have implemented high fidelity single qubit control in a 3D optical lattice by driving the atoms with resonant microwave radiation. The qubit dynamics are probed using an optical probe polarization measurement, which has allowed us to observe and optimize gate performance in nearly real-time. Gate performance across the ensemble is compromised by spatial variations in the microwave intensity and an inhomogeneous AC Stark shift of the qubit transition frequency imposed by the optical lattice. Nevertheless we are able to achieve single-qubit gates with a fidelity of 0.990(5). We have further investigated the use of composite pulses of the type used in NMR experiments, with demonstrable gain in the robustness against errors. In our system, however, the extra decoherence accrued during the longer composite pulses largely outweigh gains from added robustness, and we see no significant increase in gate performance. In a second experiment we use an optical probe polarization measurement to acquire complete information about the single atom density matrix for an ensemble of Cs atoms in the F = 3 hyperfine ground manifold. This is accomplished by continually measuring a single atomic observable (e. g. a component of the spin), while driving the system in such a way that it gradually explores the entire spin state space. The quantum state can then be estimated from the measurement record in the presence of the known system dynamics. We have shown that high fidelity estimates can be achieved for a wide variety of test states, including squeezed- and similar non-classical states generated by the action of the tensor light shift. Our estimation procedure is non-destructive, in the sense that the ensemble remains available in a known quantum state that has not decohered at the end of the estimation process. It can also in principle be performed in real time, though our current implementation remains far from that limit. This suggests that the procedure may serve as the starting point for a new type of feedback that involves partial or complete estimation of the quantum state of the ensemble.
Matthew G. Blain, Sandia National Laboratory
Abstract: We present our progress on the microfabrication and packaging of chip-scale Paul traps for applications in quantum simulation experiments. The trap electrode fabrication process, based on a MEMS fabrication technology utilizing molded tungsten, is summarized. Additionally, we discuss the implications of using high resistivity silicon as the RF trap substrate upon which the trap electrodes are formed, as well as the formation of optical access holes in the Si to allow for laser access to the traps. We also show results of the development of a custom RF chip packaging technology that maximizes optical access to the traps and provides an experimentally compatible set of materials for both chip and package.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE AC04-94AL85000.
Session #6: Fault-Tolerant Quantum Computing
John Preskill, California Institute of Technology
Abstract: The standard theory of fault-tolerant quantum computing shows that clever software design can overcome the deficiencies of noisy quantum hardware, as long as the noise is not too strong. In this lecture I will describe a different approach, in which the hardware itself is intrinsically resistant to noise. In a topological quantum computer, quantum information is encoded in the fusion spaces of nonabelian anyons in a two dimensional medium, and can be manipulated robustly by guiding the anyons along specified trajectories. If the anyons have suitable properties, the topological computer can simulate efficiently an arbitrary quantum computation.
Bryan Eastin, University of New Mexico
Abstract: I will present a procedure for calculating thresholds for quantum computation as a function of error model given the availability of ancillae with independent, identically distributed errors prepared in logical states. The thresholds are determined via a simple counting argument performed on a single qubit of an infinitely large CSS code. I give concrete examples of thresholds thus achievable for both Steane and Knill style fault tolerant implementations.
Robert Raussendorf, California Institute of Technology
Abstract: We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions [quant-ph/0510135]. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error threshold is 1.4% for local depolarizing error and 0.11\% for each source in an error model with preparation-, gate-, storage- and measurement errors. This is joint work with Jim Harrington (LANL) and Kovid Goyal (Caltech).
Session #7: Trapped Ion Quantum Information
Roee Ozeri, NIST Boulder
Abstract: Recent progress towards realizing a scalable trapped-ion quantum information processor at NIST will be reviewed. Quantum algorithms have been performed on registers of up to six ion-qubits in a multi-zone linear RF Paul trap. For example, many particle entanglement was studied by generating Schroedinger cat states of up to six ions. Steps towards achieving fault-tolerant quantum computation were implemented: memory coherence times were extended using a qubit transition which, to first order, is independent of the magnetic field. The fundamental limits to stimulated-Raman induced quantum gates were investigated by studying the effect of spontaneous scattering of photons on hyperfine coherence. More complex trap architectures and fabrication methods that will enable the scaling of ion-traps to a large multiplexed trap array are also being developed.
* Supported by DOT, ONR & NIST.
Peter Maunz, University of Michigan
Abstract: The application of ultrashort laser pulses on ions stored in a Paul trap opens up new possibilities for quantum information processing. Ultrashort pulses can be used for remote entanglement of ions via emitted photons , and to realize fast quantum gates . In this talk we present experiments demonstrating important steps toward the realization of these ideas. We show the generation of ion-photon entanglement and we demonstrate second order interference of single photons emitted from different Cadmium ions. In a second experiment we use two consecutive picosecond pi-pulses to transfer a qubit stored in the hyperfine levels of a Cadmium ion from the ground state to the excited state and back while preserving the spin coherence.
 C. Simon, and W.T.M. Irvine, PRL 91, 110405, (2003)
 J.J. Garcia-Ripoll, P. Zoller and J.l. Cirac, PRL 91, 157901, (2003)
Session #8: Fundamental Quantum Information Science
A.R.P. Rau, Louisiana State University
Abstract. Berry's geometric phase is important in quantum physics and now is central to the field of quantum computation. For spin-1/2 and its associated SU(2) group, the Bloch sphere and a U(1) phase provide a complete description. We generalize this construction to any N-level system and SU(N), setting up an iterative scheme to reduce the problem to SU(N-n). A general time-dependent Hamiltonian is thus solved, closely paralleling the SU(2) case. For n=1, each step, which involves the solution of a vector Riccati equation, · provides a U(1) phase, along with its decomposition into dynamical and geometrical parts. the technique also extends to non-Hermitian Hamiltonians and non-unitary evolution described by master equations when dissipation and decoherence are present.
Brian Smith, University of Oregon
Abstract: Coordinate-space photon wave functions and their quantum-mechanical equations of motion are presented. It is shown that the two-photon wave function is equivalent to the two-photon detection amplitude under the quantum measurement collapse hypothesis.
Shohini Ghose, Wilfrid Laurier University
Abstract: Quantum computation can be performed with continuous rather than discrete variables in an optical setting using the electromagnetic field amplitudes. Universal quantum computation requires the application of nonlinear transformations corresponding to Hamiltonians that are not linear or quadratic functions of the continuous variables. We investigate the use of non-Gaussian states as ancillary inputs in Gaussian preserving circuits for generating the required nonlinear transformations for quantum computation with continuous variables. We present a detailed analysis of a recent proposal for off-line preparation of a non-Gaussian cubic phase state . We extend our previous studies of this scheme and discuss the fidelity of preparing an ideal cubic phase state, taking into account currently achievable levels of squeezing and photodetection efficiency. Our studies indicate that although a good approximation to the ideal cubic phase states is not currently feasible! , the prepared state can nevertheless generate nonlinear gates that may be sufficient for universal quantum computation. In addition to the cubic phase state, we also analyze the use of ancilla Fock states in optical circuits. We generalize our previous results and compute the set of gates that can be implemented using such ancilla states in any circuit with Gaussian inputs, linear optics and squeezing elements, homodyne detection and feed forward. Our results show that such circuits can approximately implement a broad class of unitary gates. We also discuss the efficiency of classical simulation of such circuits. These results extend the existing no-go theorems for continuous variable quantum information processing .
 D. Gottesman, A. Kitaev and J. Preskill, Phys. Rev. A 64, 012310 (2001).
 S.D. Bartlett, B. C. Sanders, S. L. Braunstein and K. Nemoto, Phys. Rev. Lett. 88, 097904 (2002).
Masoud Mohseni, University of Toronto
Abstract: Experiments are always conducted on open systems, i.e., systems that interact with an external environment. The characterization of the dynamics of open quantum systems is a fundamental and central problem in quantum mechanics. Algorithms for performing this task are known as quantum process tomography, and typically rely on subjecting a complete set of quantum input states to the same open system dynamics. The corresponding output states are measured via a process known as quantum state tomography. Here we present an optimal algorithm for complete and direct characterization of quantum dynamics, which does not require quantum state tomography. We demonstrate a quadratic advantage in the number of ensemble measurements over all previously known quantum process tomography algorithms, and prove that this is optimal. As an application of our algorithm, we demonstrate that for a two-level quantum system that undergoes a sequence of amplitude damping and phase! damping processes, the relaxation time Tl and the dephasing time T2 can be simultaneously determined via a single measurement. Moreover, we show that generalized quantum superdense coding can be implemented optimally using our algorithm. We argue that our algorithm is experimentally implementable in a variety of prominent quantum information processing systems, and show explicitly how the algorithm can be physically realized in photonic systems with present day technology.
Kurt Jacobs, Louisiana State University
Abstract: Superselection rules (SSRs) limit the mechanical and information processing resources represented by quantum states. However SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do "logical work" due to its accessible entanglement, and its ability to act as a shared reference system.
Peter Love, DWave Inc.
Abstract: Entanglement lies behind the greater information-theoretic power of quantum systems. Shared entangled states are required for the implementation of quantum cryptographic schemes, and quantum computers require entanglement to exceed the capabilities of classical computers. We define a set of elementary entanglement monotones and give a single measure of entanglement in terms of these monotones which is zero except on globally entangled (fully inseparable) states. We describe some properties of this measure and its use to characterize the entanglement present in the ground state of four coupled flux qubits.