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- V. Bužek, M. Hillery
- 1996

We analyze a possibility of copying (≡ cloning) of arbitrary states of quantum-mechanical spin1/2 system. We show that there exists a “universal quantum-copying machine” (i.e. transformation) which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input. We also examine a machine which combines a… (More)

This is the first part of what will be a two-part review of distribution functions in physics. Here we deal with fundamentals and the second part will deal with applications. We discuss in detail the properties of the distribution function defined earlier by one of us (EPW) and we derive some new results. Next, we treat various other distribution functions.… (More)

- Mark Hillery, M Suhail Zubairy
- Physical review letters
- 2006

We provide a class of inequalities whose violation shows the presence of entanglement in two-mode systems. We initially consider observables that are quadratic in the mode creation and annihilation operators and find conditions under which a two-mode state is entangled. Further examination allows us to formulate additional conditions for detecting… (More)

- János A Bergou, Ulrike Herzog, Mark Hillery
- Physical review letters
- 2003

In quantum state filtering one wants to determine whether an unknown quantum state, which is chosen from a known set of states, [|psi(1)>, em leader,|psi(N)>], is either a specific state, say |psi(1)>, or one of the remaining states, [|psi(2)>, em leader,|psi(N)>]. We present the optimal solution to this problem, in terms of generalized measurements, for… (More)

- V. Bužek, M. Hillery
- 1999

Classical information consists of bits, each of which can be either 0 or 1. Quantum information, on the other hand, consists of qubits which are two-level quantum systems with one level labeled |0〉 and the other |1〉. Qubits can not only be in one of the two levels, but in any superposition of them as well. This fact makes the properties of quantum… (More)

The problem of discriminating among given nonorthogonal quantum states is underlying many of the schemes that have been suggested for quantum communication and quantum computing. However, quantum mechanics puts severe limitations on our ability to determine the state of a quantum system. In particular, nonorthogonal states cannot be discriminated perfectly,… (More)

- Vladimír R. Buzek, Mark Hillery
- QCQC
- 1998

We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit, and we present the corresponding quantum logic network. We also present a network for an optimal quantum copying “machine” (transformation) which produces N… (More)

- Mark Hillery
- 1998

We present the universal cloning transformation of states in arbitrary-dimensional Hilbert spaces. This unitary transformation attains the optimal fidelity of cloning as specified by Werner [Phys. Rev. A 58, 1827 (1998)]. With this cloning transformation, pure as well as impure states can be optimally copied, and the quality of the copies does not depend on… (More)

- János A Bergou, Mark Hillery
- Physical review letters
- 2005

We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers, and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with… (More)

A number of classical algorithms are based on random walks on graphs. It is hoped that recently defined quantum walks can serve as the basis for quantum algorithms that will faster than the corresponding classical ones. We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call… (More)