Showing papers by "Mark Hillery published in 2006"
TL;DR: This work provides a class of inequalities whose violation shows the presence of entanglement in two-mode systems and shows how the methods used here can be extended to find entangling in systems of more than two modes.
Abstract: 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 entanglement. We conclude by showing how the methods used here can be extended to find entanglement in systems of more than two modes.
313 citations
TL;DR: This work analyzes in detail communication privacy based on quantum resources, and proposes new quantum protocols that would lead to voting schemes that respect privacy in some situations.
138 citations
TL;DR: In this article, the authors examined the implications of several recently derived conditions for determining when a two-mode state is entangled and applied the entanglement conditions to the study of several linear devices, including the beam splitter, the parametric amplifier, and the linear phase-insensitive amplifier.
Abstract: We examine the implications of several recently derived conditions [Hillery and Zubairy, Phys. Rev. Lett. 96, 050503 (2006)] for determining when a two-mode state is entangled. We first find examples of non-Gaussian states that satisfy these conditions. We then apply the entanglement conditions to the study of several linear devices, the beam splitter, the parametric amplifier, and the linear phase-insensitive amplifier. For the first two, we find conditions on the input states that guarantee that the output states are entangled. For the linear amplifier, we determine in the limit of high and no gain, when an entangled input leads to an entangled output. Finally, we show how application of two two-mode entanglement conditions to a three-mode state can serve as a test of genuine three-mode entanglement.
96 citations
TL;DR: In this article, the authors investigate quantum walks in multiple dimensions with different quantum coins, and they augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases, enabling them to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition.
Abstract: We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts 'simplify' the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.
60 citations
TL;DR: The positive operator valued measures that solve the problem of optimally unambiguously discriminating between two subspaces of a Hilbert space and several applications, including the discrimination of multipartite states without classical communication are presented.
Abstract: We show how to optimally unambiguously discriminate between two subspaces of a Hilbert space. In particular we suppose that we are given a quantum system in either the state $\ensuremath{\mid}{\ensuremath{\psi}}_{1}⟩$, where $\ensuremath{\mid}{\ensuremath{\psi}}_{1}⟩$ can be any state in the subspace ${S}_{1}$, or $\ensuremath{\mid}{\ensuremath{\psi}}_{2}⟩$, where $\ensuremath{\mid}{\ensuremath{\psi}}_{2}⟩$ can be any state in the subspace ${S}_{2}$, and our task is to determine in which of the subspaces the state of our quantum system lies. We do not want to make any error, which means that our procedure will sometimes fail if the subspaces are not orthogonal. This is a special case of the unambiguous discrimination of mixed states. We present the positive operator valued measures that solve this problem and several applications of this procedure, including the discrimination of multipartite states without classical communication.
38 citations
TL;DR: A class of programmable devices that can discriminate between two quantum states is described and it is found that providing n>1 copies of the data state yields higher success probabilities than providing n>"1 copies" of the program states.
Abstract: We describe a class of programmable devices that can
discriminate between two quantum states. We consider two cases.
In the first, both states are unknown. One copy of each of the
unknown states is provided as an input, or program, for the two
program registers, and the data state, which is guaranteed to
be prepared in one of the program states, is fed into the data
register of the device. This device will then tell us, in an
optimal way, which of the templates stored in the program
registers the data state matches. In the second case, we know
one of the states while the other is unknown. One copy of the
unknown state is fed into the single program register, and the
data state which is guaranteed to be prepared in either the
program state or the known state, is fed into the data
register. The device will then tell us, again optimally,
whether the data state matches the template or is the known
state. We determine two types of optimal devices. The first
performs discrimination with minimum error, and the second
performs optimum unambiguous discrimination. In all cases we
first treat the simpler problem of only one copy of the data
state and then generalize the treatment to n copies. In
comparison to other works we find that providing n>1 copies of
the data state yields higher success probabilities than
providing n>1 copies of the program states.
37 citations
TL;DR: This work shows how to find the program for a given processor that produces the best approximation of a particular unitary operation and places bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.
Abstract: A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.
31 citations
TL;DR: This work generalizes the concept of quantum programmable processors and proposes programmable measurement devices, which are devices with a data register and a program register.
Abstract: A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices. We generalize the concept of quantum programmable processors and we propose programmable measurement devices.
16 citations