Past Quantum Lunches

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16 Sept. 2015, 12:00-13:00

Quantum Lunch: Quantum Circuits for Isometries

Title: Quantum Circuits for Isometries

Speaker: Raban Iten

Abstract: Every quantum operation can be decomposed into a sequence of single-qubit and Controlled-Not (C-NOT) gates. In many experimental architectures, single-qubit gates are relatively ‘cheap’ to perform compared to C-NOTs (for instance, being less susceptible to noise), and hence it is desirable to minimize the number of C-NOT gates required to implement a circuit. I will consider the task of constructing an arbitrary isometry from m qubits to n qubits, while trying to minimize the number of C-NOT gates required.  I will show a lower bound and then give an explicit gate decomposition that gets within a factor of about two of this bound. Through Stinespring’s theorem this points to a C-NOT-efficient way to perform an arbitrary quantum operation.
1 July 2015, 12:00-13:00

Quantum Lunch: Localization from superselection rules in translation invariant systems

Speaker: Isaac Kim

Abstract: We study a translation invariant spin model in a three-dimensional regular lattice, called the cubic code model, in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with finite energy are localized; the overwhelming majority of such states have energy concentrated around a finite number of defects, and remain so for a time that is near-exponential in the distance between the defects. This phenomenon is due to an emergent superselection rule and does not require any disorder. This is joint a joint work with Jeongwan haah.(1505.01480)
3 June 2015, 12:00-13:00

Quantum Lunch: Learning and testing of mixed state spectra

Speaker: John Wright
Abstract:
An experiment produces an unknown mixed state, and you would like to learn some property of this state.  How do you do this?  The standard approach is to rerun the experiment multiple times and perform some measurement on the copies produced.  The goal is then to learn or test the property using the smallest number of copies possible.  In some cases, such as performing tomography on rank one pure states, researchers have designed algorithms which are optimal in their copy complexity.  However, for many basic properties, including things as basic as estimating a mixed state's spectrum, this remains an open problem.
In this talk, we consider learning and testing properties which depend only on the mixed state's spectrum.  Natural problems in this space include learning its spectrum, estimating its von Neumann entropy, or testing whether it is low rank.  Our results include (i) a new upper bound for learning a mixed state's spectrum and (ii) an optimal algorithm for testing whether a mixed state is equal to the maximally mixed state.  We use techniques from the asymptotic theory of the symmetric group; in particular, we rely on Kerov's algebra of observables to help us study the moments of random Young diagrams.

Joint work with Ryan O'Donnell.
13 May 2015, 12:00-13:00

Quantum Lunch: An adaptive attack on Wiesner's quantum money

Speaker: Daniel Nagaj (Slovak Academy of Sciences)

Abstract:

Unlike classical money, which is hard to forge for practical reasons (e.g. producing paper with a certain property), quantum money is attractive because its security might be based on the no-cloning theorem. The first quantum money scheme was introduced by Wiesner circa 1970. Although more sophisticated quantum money schemes were proposed, Wiesner's scheme remained appealing because it is both conceptually clean and relatively easy to implement.
We show efficient adaptive attacks on Wiesner's quantum money scheme (and its variant by Bennett et al.), when valid money is accepted and passed on, while invalid money is destroyed. We propose two attacks, the first is inspired by the Elitzur-Vaidman bomb testing problem, while the second is based on the idea of protective measurements. It allows us to break Wiesner's scheme with 4 possible states per qubit, and generalizations which use more than 4 states per qubit. 
8 Apr. 2015, 12:00-13:00

Quantum Lunch

Speaker: Min-Hsiu Hsieh
Title: A Classical Analog to Entanglement Reversibility
Abstract: 
In this letter we introduce the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution pXYZ and transform secret bits back into pXYZ at equal rates using local operation and public communication (LOPC). This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the G\'{a}cs-K\"{o}rner Common Information.