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Quantum Information as Complementary Classical Information

Joseph Renes, Technical University of Darmstadt

(Session 5 : Friday from 5:00-7:00)

Abstract. Since the breakthrough by Calderbank, Shor, and Steane on the existence of quantum error-correcting codes, an oft-used notion in quantum information theory is that we can treat quantum information essentially as a strange combination of two types of classical information, pertaining to two complementary observables "amplitude" and "phase". Correcting errors afflicting either of these observables is sufficient to restore the quantum information to its original state. This approach is also appealing on a more fundamental level, as it suggests that the important differences between classical and quantum information processing originate from the phenomenon of complementarity, which is at the heart of the difference between classical and quantum mechanics. However, the central results of quantum information theory established recently, such as the achieveable rate of quantum communication over a noisy channel, follow a different approach termed decoupling which has a natural origin in the study of quantum cryptography. We show that the decoupling-based results can be concretely established in the complementary classical information picture. By adopting an information-theoretic approach to complementarity, we are able to construct entanglement distillation protocols which straightforwardly seek to distill amplitude and phase correlations without venturing into decoupling. This gives new and intuitive proofs of both the noisy channel coding theorem and the asymptotic rates of both secret-key distillation and state merging. Joint work with J.-C. Boileau.

Measurement-Based Quantum Computation in Realistic Spin-1 Chains

Joseph Renes, Technical University of Darmstadt

(Session 9 : Saturday from 3:30-4:00)

Abstract. The excitement surrounding meausrement-based quantum computation comes not just from the intriguing theoretical result that the power of a quantum computer can be attributed to the nature of the initial state, but also the more practical feature that it might be possible to find or engineer physical systems which would naturally provide such initial states as ground states. Since no system can be controlled or engineered perfectly, it is therefore vital to develop methods which characterize how suitable a given physical system is for this purpose. Moreover, this must be done in a way which circumvents the apparent need to evaluate the result for arbitrary computational measurement sequences, as these grow exponentially in number. We study this problem at the single-qubit level for the hybrid scheme recently introduced by Brennen and Miyake [1] using gapped one-dimensional spin-1 AKLT chains. Here individual qubit gates are performed by measurement while two-qubit gates are performed by dynamically coupling different chains. Brennen and Miyake describe a implementations using either atoms or polar molecules in optical lattices, where the gap is expected to help suppress decoherence. We show that the approach taken by Doherty and Bartlett to characterize the computational power of nearly-cluster state quantum computers [2] can be profitably adapted to this case, avoiding the exponential counting trap mentioned above. By numerical and perturbative analysis we find that arbitrary single-qubit operations can be faithfully executed over a reasonbly wide parameter range of bilinear-biquadratic Hamiltonians near the AKLT point. Furthermore, we find that the Doherty-Bartlett approach leads directly to the use of string order parameters, showing a connection between computational questions and the traditional theoretical study of condensed matter, where these parameters arise. Joint work with Stephen Bartlett, Gavin Brennen, and Akimasa Miyake. [1] Brennen and Miyake, Phys. Rev. Lett. 101, 010502 (2008). [2] Doherty and Bartlett, arXiv:0802.4314v1 [quant-ph].