Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations

We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum operations is required in our scheme. We further show that our scheme is optimal in the sense that the number of the runs is minimal when discriminating only two unitary operations.Comment: 4 pages(in Revtex4), 2 figures (eps). Corrected some typos and two equations. Main results unchanged. Essentially the journal versio

Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels $N$ that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small $N$, that exceed the known bound for the Leggett-Garg inequality, and show that in the limit $N\rightarrow \infty$ the Leggett-Garg inequality can be violated up to its algebraic maximum.Comment: 6 pages, 2 figure

Quantum data gathering

Measurement of a quantum system – the process by which an observer gathers information about it – provides a link between the quantum and classical worlds. The nature of this process is the central issue for attempts to reconcile quantum and classical descriptions of physical processes. Here, we show that the conventional paradigm of quantum measurement is directly responsible for a well-known disparity between the resources required to extract information from quantum and classical systems. We introduce a simple form of quantum data gathering, “coherent measurement”, that eliminates this disparity and restores a pleasing symmetry between classical and quantum statistical inference. To illustrate the power of quantum data gathering, we demonstrate that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states)

Quantum Cloning Machines and the Applications

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published online

Probabilistic theories with purification

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows one to prove most of the basic features of quantum mechanics, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.Comment: Differing from the journal version, this version includes a table of contents and makes extensive use of boldface type to highlight the contents of the main theorems. It includes a self-contained introduction to the framework of general probabilistic theories and a discussion about the role of causality and local discriminabilit