Experimental verification of the commutation relation for Pauli spin operators using single-photon quantum interference

We report experimental verification of the commutation relation for Pauli spin operators using quantum interference of the single-photon polarization state. By superposing the quantum operations $\sigma_z \sigma_x$ and $\sigma_x \sigma_z$ on a single-photon polarization state, we have experimentally implemented the commutator, $[\sigma_{z}, \sigma_{x}]$, and the anticommutator, $\{\sigma_{z}, \sigma_{x}\}$, and have demonstrated the relative phase factor of $\pi$ between $\sigma_z \sigma_x$ and $\sigma_x \sigma_z$ operations. The experimental quantum operation corresponding to the commutator, $[\sigma_{z}, \sigma_{x}]=k\sigma_y$, showed process fidelity of 0.94 compared to the ideal $\sigma_y$ operation and $|k|$ is determined to be $2.12\pm0.18$.Comment: 4pages, 3 figure

Reversing the Weak Quantum Measurement for a Photonic Qubit

We demonstrate the conditional reversal of a weak (partial-collapse) quantum measurement on a photonic qubit. The weak quantum measurement causes a nonunitary transformation of a qubit which is subsequently reversed to the original state after a successful reversing operation. Both the weak measurement and the reversal operation are implemented linear optically. The state recovery fidelity, determined by quantum process tomography, is shown to be over 94% for partial-collapse strength up to 0.9. We also experimentally study information gain due to the weak measurement and discuss the role of the reversing operation as an information erasure

Realizing Physical Approximation of the Partial Transpose

The partial transpose by which a subsystem's quantum state is solely transposed is of unique importance in quantum information processing from both fundamental and practical point of view. In this work, we present a practical scheme to realize a physical approximation to the partial transpose using local measurements on individual quantum systems and classical communication. We then report its linear optical realization and show that the scheme works with no dependence on local basis of given quantum states. A proof-of-principle demonstration of entanglement detection using the physical approximation of the partial transpose is also reported.Comment: 5 pages with appendix, 3 figure

Experimental Implementation of the Universal Transpose Operation

The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.Comment: 4 pages, 4 figure

A Guide to Navigating Existing and Emerging Sources of Local VMT and Travel Data

As the crisis of climate change looms, transportation policy in California continues to emphasize sustainability in land-use and transportation decisions. This report evaluates the implementation of two sustainability-focused policies (Senate Bill 375 and 743) by local governments and the current-state-of-the-practices by metropolitan planning organizations (MPOs) in assisting them in California. The research focuses on local governments’ access and use of vehicle miles traveled (VMT) and transportation data for achieving VMT and greenhouse gas (GHG) reduction by land-use planning. The research also examines the role of MPOs in providing needed transportation data, training, and technical support to its local members to help them quantify VMT impacts of land-use plans and projects. Through surveys and interviews of 539 city and county governments and 18 MPOs in California, the research team analyzes current practices. Findings include that local governments utilize automobile data more frequently than alternative modes, and do not heavily rely on MPOs for obtaining transportation data. Local governments recognized the need for more transportation data and were particularly interested in publicly available sources. The MPOs reported that VMT/annual average daily traffic data and origin-destination matrix were most frequently requested. More sophisticated data such as travel-time matrix and mode-share scheme were considered useful by the MPOs, while requests were very low. Based on the results of the conducted surveys, interviews, and our analyses, we developed a transportation data guide for local governments that could help them access data for achieving VMT/GHG emission reduction via land-use planning. The guide has two parts, one for general plan update and any land-use plans along with SB 375 and the other for VMT analysis for project-level California Environmental Quality Act reviews. The guide includes several different approaches that can be chosen and tried by local governments depending on their resource level and geographic, social, and physical characteristics. These findings can facilitate the access and use of transportation data to aid in sustainable land-use planning for the betterment of local communities and the planet