Upper Bound on the region of Separable States near the Maximally Mixed State

A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of subsystems, and dimensions of Hilbert space, and is shown to be exact for qubits. The new bound is compared to previous such bounds on this quantity, and found to be stronger in all cases. It implies that increasing the number of subsystems, rather than increasing their Hilbert space dimension is a more effective way of increasing entanglement. An explicit decomposition into an ensemble of separable states, when the state is not entangled,is given for the case of qubits.Comment: 2 figures. accepted J. Opt. B: Quantum Semiclass. Opt. (2000

Adiabatic quantum computation along quasienergies

The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of a parameter |v>, which is available to adjust the gaps of the quasienergies to control the running time steps. In Grover's database search problem, the costs to prepare |v> for the qualitatively different, i.e., power or exponential, running time steps are shown to be qualitatively different. Curiously, in establishing the equivalence between the standard quantum computation based on the circuit model and the anholonomic adiabatic quantum computation model, it is shown that the cost for |v> to enlarge the gaps of the eigenvalue is qualitatively negligible.Comment: 11 pages, 2 figure

SU(N) Coherent States

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.Comment: 25 pages, LaTex, no figure

Entanglement detection from interference fringes in atom-photon systems

A measurement scheme of atomic qubits pinned at given positions is studied by analyzing the interference pattern obtained when they emit photons spontaneously. In the case of two qubits, a well-known relation is revisited, in which the interference visibility is equal to the concurrence of the state in the infinite spatial separation limit of the qubits. By taking into account the super-radiant and sub-radiant effects, it is shown that a state tomography is possible when the qubit spatial separation is comparable to the wavelength of the atomic transition. In the case of three qubits, the relations between various entanglement measures and the interference visibility are studied, where the visibility is defined from the two-qubit case. A qualitative correspondence among these entanglement relations is discussed. In particular, it is shown that the interference visibility is directly related to the maximal bipartite negativity.Comment: 12 pages, 2 figures, published versio

Overcoming decoherence in the collapse and revival of spin Schr\"odinger cats

In addition to being a very interesting quantum phenomenon, Schr\"odinger cat swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a cat-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schr\"odinger cat, which could be of significant utility in quantum metrology and other quantum processing.Comment: 4 pages, 2 figure

Quantum Dynamics of Three Coupled Atomic Bose-Einstein Condensates

The simplest model of three coupled Bose-Einstein Condensates (BEC) is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean field approximation. This semiclassical analysis using the system symmetries shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points and our analysis shows the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays the dynamical transition. The quantum case has collapse and revival sequences superposed on the semiclassical dynamics reflecting the underlying discreteness of the spectrum. Non-zero circular current states are also demonstrated as one of the higher dimensional effects displayed in this system.Comment: Accepted to PR

Qudit Quantum State Tomography

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First we show how non-orthogonal measurement allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum state tomography can be performed for multi qudits with a specific example illustrating how to achieve this in one and two qutrit systems.Comment: 6 pages, 4 figures, submitted to PR

Spectral Effects of Strong Chi-2 Non-Linearity for Quantum Processing

Optical $\chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong $\chi^{(2)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong $\chi^{(2)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.Comment: Will be submitted to PR

Modified TAP equations for the SK spin glass

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed.Comment: 7 pages, 2 figures, final revised version to appear in Europhys. Let