Program
Full Program | Thursday | Friday | Saturday | All Sessions | Posters | Talks
SESSION 9c: Kaleidoscope of QI theoretical frontiers (Enchantment E-F)Chair: Jim Harrington (HRL) | |
| 4:00 pm - 4:30 pm | Mark Wilde, (Louisiana) Recoverability in quantum information theory | Abstract. The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Furthermore, the recovery operation has an explicit form and is universal, in the sense that it depends only on the channel and the state which can be perfectly recovered. Our proof method relies on complex interpolation and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This submission is based on the following two papers: [1] Mark M. Wilde. "Recoverability in quantum information theory," Proceedings of the Royal Society A, vol. 471, no. 2182, page 20150338 October 2015 [2] Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, Andreas Winter. "Universal recovery from a decrease of quantum relative entropy", arXiv:1509.07127. |
| 4:30 pm - 5:00 pm | Jonathan A. Gross, Caves group (New Mexico) Fisher symmetry and the geometry of quantum states | Abstract. The quantum Fisher information (QFI) is a valuable tool on account of the achievable lower bound it provides for single-parameter estimation. Due to the existence of incompatible quantum observables, however, the lower bound provided by the QFI cannot be saturated in the general multi-parameter case. A bound demonstrated by Gill and Massar (GM) captures some of the limitations that incompatibility imposes in the multi-parameter case. We further explore the structure of measurements allowed by quantum mechanics, identifying restrictions beyond those given by the QFI and GM bound. These additional restrictions give insight into the geometry of quantum state space and notions of measurement symmetry related to the QFI. |
| 5:00 pm - 5:30 pm | Martin Roetteler, (Microsoft) Reversible circuit compilation with space constraints | Abstract. We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to “garbage collection” for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett's method, REVS can reduce space complexity by a factor of 4 or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks. |
| 5:30 pm - 6:00 pm | Jacob Miller, Miyake group (New Mexico) Quantum computation using genuine two-dimensional symmetry-protected topological order | Abstract. We extend the connection between degenerate entanglement spectra present in symmetry-protected topological orders (SPTO's) of 1D spin chains and their use in measurement-based quantum computation (MQC) to the setting of 2D systems. We find surprisingly that the 2D cluster state, an archetypal resource state for MQC, is in a trivial 2D SPTO phase, and show, by a more fine-grained classification, that it does have nontrivial SPTO, but of the same nature as 1D spin chains. In contrast, we introduce a new ground state which possesses nontrivial SPTO entirely of a 2D nature, and show that it is universal for MQC. By utilizing genuine higher-dimensional SPTO, our results open up a research avenue to directly harness its greater quantum-gate complexity within the so-called Clifford hierarchy for the first time in MQC. |
| 6:00 pm - 6:30 pm | Grant Salton, Hayden group (Stanford) Spacetime replication of continuous variable quantum information | Abstract. The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically-constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics. |
SQuInT Chief Organizer
Prof. Akimasa Miyake
amiyake@unm.edu
SQuInT Co-Organizer
Prof. Elohim Becerra
fbecerra@unm.edu
SQuInT Founder
Prof. Ivan Deutsch
ideutsch@unm.edu
SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850
