Quantum Computing with Noninteracting Particles
Alex Arkhipov Massachusetts Institute of Technology (MIT)
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The invasion of physics by information theory
Robert Spekkens Perimeter Institute for Theoretical Physics
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Ambiguities in order-theoretic formulations of thermodynamics
Harvey Brown University of Oxford
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A histories perpective on bounding quantum correlations
Joe Henson BNP Paribas Asset Management London
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Seeing is Believing: Direct Observation of a General Quantum State
Jeff Lundeen University of Ottawa
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Maximal Privacy Without Coherence
Debbie Leung Institute for Quantum Computing (IQC)
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Probabilistic protocols in quantum information
Joshua Combes University of Colorado Boulder
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Bosonic particle-correlated states
Zhang Jiang University of New Mexico
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Quantum Computing with Noninteracting Particles
Alex Arkhipov Massachusetts Institute of Technology (MIT)
We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very limited nature of the model, an exact classical simulation would imply a collapse of the polynomial hierarchy. Moreover, under plausible conjectures, a "noisy" approximate simulation would do the same. This gives evidence that quantum computers can sample a distribution that classical computers cannot even approximate, even when restricted to use no entanglement except that arising from particles being identical. We briefly discuss experimental prospects for realizing this model. This talk is based on The Computational Complexity of Linear Optics [STOC '11], which is joint work with Scott Aaronson. -
Incompatibility of observables in quantum theory and other probabilistic theories
We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories. This opens up a flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have. In particular, we prove that two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible. However, if one adopts a more refined measure of the degree of incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories whose inherent degree of incompatibility is greater than that of quantum theory. Finally, we analyze the noise tolerance of the incompatibility of a pair of observables in a CHSH-Bell experiment. -
The invasion of physics by information theory
Robert Spekkens Perimeter Institute for Theoretical Physics
When we think of a revolution in physics, we usually think of a physical theory that manages to overthrow its predecessor. There is another kind of revolution, however, that typically happens more slowly but that is often the key to achieving the first sort: it is the discovery of a novel perspective on an existing physical theory. The use of least-action principles, symmetry principles, and thermodynamic principles are good historical examples. It turns out that we can refine our understanding of many of these principles by characterizing certain properties of physical states as resources. I will discuss some of the highlights of two resource theories: the resource theory of asymmetry, which characterizes the relations among quantum states that break a symmetry; and the resource theory of athermality, which characterizes the relations among quantum states that deviate from thermal equilibrium. In particular, I will discuss how Noether's theorem does not capture all of the consequences of symmetries of the dynamics, and how the second law of thermodynamics does not capture all of the constraints on thermodynamic transitions. Finally, I will show that both asymmetry and athermality are informational resources, and that rehabilitated versions of Noether's theorem and the second law can both be understood as constraints on data processing. Considerations such as these---as well as evidence from other fronts of the invasion---make a compelling case for the revolutionary cause of reconceiving physics from an information-theoretic perspective. -
Ambiguities in order-theoretic formulations of thermodynamics
Harvey Brown University of Oxford
Since the 1909 work of Carathéodory, an axiomatic approach to thermodynamics has gained ground which highlights the role of the the binary relation of adiabatic accessibility between equilibrium states. A feature of Carathédory's system is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law. This talk attempts first to clarify the nature of this ambiguity, by defining the arrow of time in thermodynamics by way of the Equilibrium Principle (``Minus First Law''). It then examines the extent to which the 1989 axiomatisation of Lieb and Yngvason shares the same ambiguity, despite proposing a very different approach to the second law. -
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
Roger Mong University of Pittsburgh
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. The Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support Ising non-Abelian anyons, also referred to as Majorana zero modes. Here we construct a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles, and like the Z3 Read-Rezayi state, harbors Fibonacci anyons that--unlike Ising anyons--allow for universal topological quantum computation solely through braiding. -
A histories perpective on bounding quantum correlations
Joe Henson BNP Paribas Asset Management London
There has recently been much interest in finding simple principles that explain the particular sets of experimental probabilities that are possible with quantum mechanics in Bell-type experiments. In the quantum gravity community, similar questions had been raised, about whether a certain generalisation of quantum mechanics allowed more than quantum mechanics in this regard. We now bring these two strands of work together to see what can be learned on both sides. -
Seeing is Believing: Direct Observation of a General Quantum State
Jeff Lundeen University of Ottawa
Central to quantum theory, the wavefunction is a complex distribution associated with a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate measurement outcome probabilities through the Born Rule. Tomographic methods can reconstruct the wavefunction from measured probabilities. In contrast, I present a method to directly measure the wavefunction so that its real and imaginary components appear straight on our measurement apparatus. I will also present new work extending this concept to mixed quantum states. This extension directly measures a little-known proposal by Dirac for a classical analog to a quantum operator. Furthermore, it reveals that our direct measurement is a rigorous example of a quasi-probability phase-space (i.e. x,p) distribution that is closely related to the Q, P, and Wigner functions. Our direct measurement method gives the quantum state a plain and general meaning in terms of a specific set of simple operations in the lab. -
Maximal Privacy Without Coherence
Debbie Leung Institute for Quantum Computing (IQC)
Privacy and coherence have long been considered closely related properties of a quantum state. Indeed, a coherently transmitted quantum state is inherently private. Surprisingly, coherent quantum communication is not always required for privacy: there are quantum channels that are too noisy to transmit quantum information but it can send private classical information. Here, we ask how different the private classical and the quantum capacities can be. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private classical capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence. -
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states
Matthew Leifer Chapman University
The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if every pair of pure states corresponds to a pair of measures that do not overlap, and is otherwise epistemic. Recently, several authors have derived theorems that aim to show that the quantum state must be ontic in this framework. Each of these theorems involve auxiliary assumptions of varying degrees of plausibility. Without such assumptions, it has been shown that models exist in which the quantum state is epistemic. However, the definition of an epistemic quantum state used in these works is extremely permissive. Only two quantum states need correspond to overlapping measures and furthermore the amount of overlap may be arbitrarily small. In order to provide an explanation of quantum phenomena such as no-cloning and the indistinguishability of pure states, the amount of overlap should be comparable to the inner product of the quantum states. In this talk, I show, without making auxiliary assumptions, that the ratio of overlap to inner product must go to zero exponentially in Hilbert space dimension for some families of states. This is done by connecting the overlap to Kochen-Specker noncontextuality, from which we infer that any contextuality inequality gives a bound on the ratio of overlap to inner product. -
Probabilistic protocols in quantum information
Joshua Combes University of Colorado Boulder
Probabilistic protocols in quantum information are an attempt to improve performance by occasionally reporting a better result than could be expected from a deterministic protocol. Here we show that probabilistic protocols can never improve performance beyond the quantum limits on the corresponding deterministic protocol. To illustrate this result we examine three common probabilistic protocols: probabilistic amplification, weak value amplification, and probabilistic metrology. In each of these protocols we show explicitly that the optimal deterministic protocol is better than the corresponding probabilistic protocol when the probabilistic nature of the protocol is correctly accounted for. -
Applications of Information Theory in Direct Sum and Direct Product Problems
A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k. In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work. -
Bosonic particle-correlated states
Zhang Jiang University of New Mexico
Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new
set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d& times;n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. For fixed d, the parameter space of our state does not grow with N. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model.