112 research outputs found
Parametrization of projector-based witnesses for bipartite systems
Entanglement witnesses are nonpositive Hermitian operators which can detect
the presence of entanglement. In this paper, we provide a general
parametrization for orthonormal basis of and use it to
construct projector-based witness operators for entanglement detection in the
vicinity of pure bipartite states. Our method to parameterize entanglement
witnesses is operationally simple and could be used for doing symbolic and
numerical calculations. As an example we use the method for detecting
entanglement between an atom and the single mode of quantized field, described
by the Jaynes-Cummings model. We also compare the detection of witnesses with
the negativity of the state, and show that in the vicinity of pure stats such
constructed witnesses able to detect entanglement of the state.Comment: 12 pages, four figure
Fermionic Linear Optics Revisited
We provide an alternative view of the efficient classical simulatibility of
fermionic linear optics in terms of Slater determinants. We investigate the
generic effects of two-mode measurements on the Slater number of fermionic
states. We argue that most such measurements are not capable (in conjunction
with fermion linear optics) of an efficient exact implementation of universal
quantum computation. Our arguments do not apply to the two-mode parity
measurement, for which exact quantum computation becomes possible, see
quant-ph/0401066.Comment: 16 pages, submitted to the special issue of Foundation of Physics in
honor of Asher Peres' 70th birthda
Test for entanglement using physically observable witness operators and positive maps
Motivated by the Peres-Horodecki criterion and the realignment criterion we
develop a more powerful method to identify entangled states for any bipartite
system through a universal construction of the witness operator. The method
also gives a new family of positive but non-completely positive maps of
arbitrary high dimensions which provide a much better test than the witness
operators themselves. Moreover, we find there are two types of positive maps
that can detect 2xN and 4xN bound entangled states. Since entanglement
witnesses are physical observables and may be measured locally our construction
could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl
Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits
Quantum phase estimation is a corner-stone in quantum algorithm design, al-lowing for the inference of eigenvalues of exponentially-large sparse matrices. The maximum rate at which these eigenvalues may be learned, -known as the Heisen-berg limit-, is constrained by bounds on the circuit complexity required to simulate an arbitrary Hamiltonian. Single-control qubit variants of quantum phase estima-tion that do not require coherence between experiments have garnered interest in re-cent years due to lower circuit depth and minimal qubit overhead. In this work we show that these methods can achieve the Heisenberg limit, also when one is un-able to prepare eigenstates of the system. Given a quantum subroutine which pro-vides samples of a 'phase function' g(k) = sigma(j) A(j)e(i Phi)j(k) with unknown eigenphases phi(j )and overlaps A(j )at quantum cost O(k), we show how to estimate the phases {phi(j}) with (root-mean-square) error delta for total quantum cost T = O(delta(-1)). Our scheme com-bines the idea of Heisenberg-limited multi -order quantum phase estimation for a single eigenvalue phase [1, 2] with subroutines with so-called dense quantum phase estimation which uses classical processing via time-series analysis for the QEEP problem [3] or the matrix pencil method. For our algorithm which adaptively fixes the choice for k in g(k) we prove Heisenberg -limited scaling when we use the time-series/QEEP subroutine. We present numerical evidence that using the matrix pencil technique the algorithm can achieve Heisenberg-limited scaling as well.Theoretical Physic
Distinguishing multi-partite states by local measurements
We analyze the distinguishability norm on the states of a multi-partite
system, defined by local measurements. Concretely, we show that the norm
associated to a tensor product of sufficiently symmetric measurements is
essentially equivalent to a multi-partite generalisation of the non-commutative
2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of
domination depend only on the number of parties but not on the Hilbert spaces
dimensions.
We discuss implications of this result on the corresponding norms for the
class of all measurements implementable by local operations and classical
communication (LOCC), and in particular on the leading order optimality of
multi-party data hiding schemes.Comment: 18 pages, 6 figures, 1 unreferenced referenc
Spectral estimation for Hamiltonians: A comparison between classical imaginary-time evolution and quantum real-time evolution
We consider the task of spectral estimation of local quantum Hamiltonians. The spectral estimation is performed by estimating the oscillation frequencies or decay rates of signals representing the time evolution of states. We present a classical Monte Carlo (MC) scheme which efficiently estimates an imaginary-time, decaying signal for stoquastic (i.e. sign-problem-free) local Hamiltonians. The decay rates in this signal correspond to Hamiltonian eigenvalues (with associated eigenstates present in an input state) and can be extracted using a classical signal processing method like ESPRIT. We compare the efficiency of this MC scheme to its quantum counterpart in which one extracts eigenvalues of a general local Hamiltonian from a real-time, oscillatory signal obtained through quantum phase estimation circuits, again using the ESPRIT method. We prove that the ESPRIT method can resolve S = poly(n) eigenvalues, assuming a 1/poly(n) gap between them, with poly(n) quantum and classical effort through the quantum phase estimation circuits, assuming efficient preparation of the input state. We prove that our Monte Carlo scheme plus the ESPRIT method can resolve S = O(1) eigenvalues, assuming a 1/poly(n) gap between them, with poly(n) purely classical effort for stoquastic Hamiltonians, requiring some access structure to the input state. However, we also show that under these assumptions, i.e. S = O(1) eigenvalues, assuming a 1/poly(n) gap between them and some access structure to the input state, one can achieve this with poly(n) purely classical effort for general local Hamiltonians. These results thus quantify some opportunities and limitations of Monte Carlo methods for spectral estimation of Hamiltonians. We numerically compare the MC eigenvalue estimation scheme (for stoquastic Hamiltonians) and the quantum-phase-estimation-based eigenvalue estimation scheme by implementing them for an archetypal stoquastic Hamiltonian system: the transverse field Ising chain
Quantum data hiding with spontaneous parameter down-conversion
Here we analyze the practical implication of the existing quantum data hiding
protocol with Bell states produced with optical downconverter. We show that the
uncertainty for the producing of the Bell states with spontaneous parameter
down-conversion should be taken into account, because it will cause serious
trouble to the hider encoding procedure. A set of extended Bell states and a
generalized Bell states analyzer are proposed to describe and analyze the
possible states of two photons distributing in two paths. Then we present a
method to integrate the above uncertainty of Bell states preparation into the
dating hiding procedure, when we encode the secret with the set of extended
Bell states. These modifications greatly simplify the hider's encoding
operations, and thus paves the way for the implementation of quantum data
hiding with present-day quantum optics.Comment: 4 pages, 1 figure, adding some analyse for security proof, to be
appear in Phys. Rev.
Irreversible Quantum Baker Map
We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.Comment: 4 pages, 3 figures include
Some Properties of the Computable Cross Norm Criterion for Separability
The computable cross norm (CCN) criterion is a new powerful analytical and
computable separability criterion for bipartite quantum states, that is also
known to systematically detect bound entanglement. In certain aspects this
criterion complements the well-known Peres positive partial transpose (PPT)
criterion. In the present paper we study important analytical properties of the
CCN criterion. We show that in contrast to the PPT criterion it is not
sufficient in dimension 2 x 2. In higher dimensions we prove theorems
connecting the fidelity of a quantum state with the CCN criterion. We also
analyze the behaviour of the CCN criterion under local operations and identify
the operations that leave it invariant. It turns out that the CCN criterion is
in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte
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