Decomposition of the efficiency of the Chinese state-owned commercial banks at the provincial level

This study adopts a bank production function approach to the measurement of banking efficiency at the provincial level in the Chinese state-owned commercial banking sector from 1998 to 2003. Applying Data Envelopment Analysis and efficiency decomposition analysis, this paper has revealed a significant level of pure technical input inefficiency and, to a lesser extent, scale inefficiency across the provincial branches of all the banking groups. The study has also uncovered the extent of inefficiency in individual banking inputs and provincial branches. Finally, the provincial-level efficiency is further decomposed into within-banking-group and between-banking-group effects

Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information

We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how the intrinsic uncertainty in a mixed quantum state is used to improve existing uncertainty relations and how this information affects one's ability to witness EPR-steering. As an example, we consider the recent improvement (using a quantum memory) to the entropic uncertainty relation between pairs of discrete observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of the tighter bound in the steering inequality leads to contradictions, due in part to the fact that the improved bound depends explicitly on the state being measured. By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one can use the information about the quantum state to improve our ability to witness EPR-steering, and develop a new symmetric EPR-steering inequality as a result.Comment: 6 page

Uncertainty Relation for Mutual Information

We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.Comment: 6 pages, 2 figure

Bounding the entanglement of N qubits with only four measurements

We introduce a new measure for the genuinely N-partite (all-party) entanglement of N-qubit states using the trace distance metric, and find an algebraic formula for the GHZ-diagonal states. We then use this formula to show how the all-party entanglement of experimentally produced GHZ states of an arbitrary number of qubits may be bounded with only four measurements

Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.Comment: 4 pages, 6 figure

Quantum Fully Homomorphic Encryption With Verification

Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page