Z. Kurucz

Continuous variable remote state preparation

We extend exact deterministic remote state preparation (RSP) with minimal classical communication to quantum systems of continuous variables. We show that, in principle, it is possible to remotely prepare states of an ensemble that is parametrized by infinitely many real numbers---i.e., by a real function---while the classical communication cost is one real number only. We demonstrate continuous variable RSP in three examples using (i) quadrature measurement and phase-space displacement operations, (ii) measurement of the optical phase and unitaries shifting the same, and (iii) photon counting and photon number shift.

General criterion for oblivious remote state preparation

A necessary and sufficient condition is given for general exact remote state preparation (RSP) protocols to be oblivious, that is, no information about the target state can be retrieved from the classical message. A criterion in terms of commutation relations is also derived for the existence of deterministic exact protocols in which Alices measurement eigenstates are related to each other by fixed linear operators similar to Bobs unitaries. For nonmaximally entangled resources, it provides an easy way to search for RSP protocols. As an example, we show how to reduce the case of partially entangled resources to that of maximally entangled ones, and we construct RSP protocols exploiting the structure of the irreducible representations of Abelian groups.

Spectroscopic properties of inhomogeneously broadened spin ensembles in a cavity

The enhanced collective coupling to weak quantum fields may turn atomic or spin ensembles into an important component in quantum information processing architectures. Inhomogeneous broadening can, however, significantly reduce the coupling and the lifetime of the collective excitation that represent the quantum information. In this paper we show that the width and shape of the inhomogeneous broadening have a striking influence on the dynamics of the cavity-ensemble system and may lead to narrowing of the linewidth of the collective states. We underpin our findings with the examples of a Gaussian and a Lorentzian profile of the inhomogeneity.

Preparable ensembles for remote state preparation

We determine all the ensembles that can be remotely prepared in a deterministic and oblivious way using a nonmaximally entangled resource with minimum classical communication cost when Bobs unitary transformations form a cyclic group. We show that the classical communication has maximal informational entropy. We also give a constraint for the shared entangled resource that can be used for remote state preparation.

Continuous-variable versus electromagnetically-induced-transparency-based quantum memories

We discuss a general model of a quantum memory for a single light mode in a collective mode of atomic oscillators. The model includes interaction Hamiltonians that are of second order in the canonical position and momentum operators of the lightand atomic oscillator modes. We also consider the possibility of measurement and feedback. We identify an interaction Hamiltonian that leads to an ideal mapping by pure unitary evolution and compare several schemes which realize this mapping using a common continuous-variable description. In particular we discuss schemes based on the off-resonant Faraday effect supplemented by measurement and feedback and proper preparation of the atoms in a squeezed state and schemes based on off-resonant Raman coupling as well as electromagnetically induced transparency (EIT).

Quantized recurrence time in unital iterated open quantum dynamics

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite-dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete-time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a superoperator (quantum channel) in each time step followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the part of the Hilbert space explored by the system, then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work shows that the expected return time is a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state.

Dynamics of the collective modes of an inhomogeneous spin ensemble in a cavity

We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves, and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wavenumber without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wavenumbers. In particular, we show that collective excitations with a well-defined wavenumber pass without dispersion from negative to positive-valued wavenumbers without populating the zero wavenumber spin wave mode. The results are relevant for multimode collective quantum memories where qubits are encoded in different spin waves.

Remote state preparation in quadrature basis

We present a theoretical scheme for non-teleportation-based exact deterministic remote state preparation (RSP) in continuous variable (CV) quantum systems. It is an infinite dimensional generalization of RSP of equatorial states. It is capable of preparing states of an ensemble that is parameterized by infinitely many real numbers, i.e. by a real function, while the classical communication cost is only one real number. We show the relation of our scheme to the classical Vernam cipher (one-time pad).

Simulating measurement statistics in remote state preparation

Exact deterministic remote state preparation schemes that involve projective measurements on Alice’s side are not able to prepare arbitrary states but a restricted ensemble of states only. Instead of restoring the output state, Bob can transform his future measuring devices, and he can get the same probability amplitudes as with the original state. We show that such a simulation of measurement statistics is not possible for arbitrary states.