Purification of Gaussian maximally mixed states

L.-M. Duan, G. Giedke, J. I. Cirac +1 more

Summary form only given. One of the key elements of quantum communication is the generation of maximally entangled states between distant nodes of a quantum network. We present an entanglement purification scheme which generates maximally entangled states in finite Hilbert spaces from the continuous two-mode squeezed states. With high probabilities, we get a more entangled stale, and the entanglement in the continuous partially entangled state is transferred to the maximally entangled states with high efficiency. Furthermore, in several practical cases this purification protocol can be readily extended to distill maximally entangled states from the mixed Gaussian continuous states.

Ingemar Bengtsson, Karol Życzkowski

Francesco Anna Mele, Filippo Girardi, Senrui Chen +2 more

The random purification channel, which, given $n$ copies of an unknown mixed state $ρ$, prepares $n$ copies of an associated random purification, has proved to be an extremely valuable tool in quantum information theory. In this work, we construct a Gaussian version of this channel that, given $n$ copies of a bosonic passive Gaussian state, prepares $n$ copies of one of its randomly chosen Gaussian purifications. The construction has the additional advantage that each purification has a mean photon number which is exactly twice that of the initial state. Our construction relies on the characterisation of the commutant of passive Gaussian unitaries via the representation theory of dual reductive pairs of unitary groups.

L.-M. Duan, G. Giedke, J. I. Cirac +1 more

We describe an entanglement purification protocol to generate maximally entangled states with high efficiencies from two-mode squeezed states or from mixed Gaussian continuous entangled states. The protocol relies on a local quantum nondemolition measurement of the total excitation number of several continuous variable entangled pairs. We propose an optical scheme to do this kind of measurement using cavity enhanced cross-Kerr interactions.

Ingemar Bengtsson, Karol Życzkowski

Carolyn Zhang, Etienne Granet

We consider how a maximally mixed state evolves under $(1+1)D$ Floquet non-unitary circuits with an antiunitary symmetry that squares to identity, that serves as a generalized $\mathcal{PT}$ symmetry. Upon tuning a parameter, the effective Hamiltonian of the Floquet operator demonstrates a symmetry breaking transition. We show that this symmetry breaking transition coincides with different kinds of purification transitions. Gaussian non-unitary circuits are mixed (not purifying) on both sides of the symmetry breaking transition, while interacting but integrable non-unitary circuits are mixed on the symmetric side and ``weakly purifying" on the symmetry breaking side. In the weakly purifying phase, the initial mixed state purifies on a time scale proportional to the system size. We obtain numerically the critical exponents associated with the divergence of the purification time at the purification transition, which depend continuously on the parameters of the model. Upon adding a symmetric perturbation that breaks integrability, the weakly purifying phase becomes strongly purifying, purifying in a time independent of the system size, for sufficiently large system size. Our models have an extra $U(1)$ symmetry that divides the Hilbert space into different magnetization sectors, some of which demonstrate logarithmic scaling of entanglement in the weakly purifying phase.