Superbroadcasting of mixed states

arXiv preprint quant-ph/0510155, 2005

Abstract:" Broadcasting", namely distributing information over many users, suffers in-principle limitations when the information is quantum. This poses a critical issue in quantum information theory, for distributed processing and networked communications. For pure states ideal broadcasting coincides with the so-called" quantum cloning", describing an hypothetical ideal device capable of producing from a finite number N of copies of a state (drawn from a set) a larger number M> N of output copies of the same state. Since such a ...

Physical Review A - PHYS REV A, 2006

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N-->M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and phase-covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.

2006

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N → M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and the phase covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.

New Journal of Physics, 2006

We consider the problem of broadcasting quantum information encoded in the average value of the field from N to M > N copies of mixed states of radiation modes. We derive the broadcasting map that preserves the complex amplitude, while optimally reducing the noise in conjugate quadratures. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting). We prove similar results for purification (M ≤ N) and for phase-conjugate broadcasting.

2006

We consider the problem of broadcasting quantum information encoded in the average value of the field from N to M>N copies of mixed states of radiation modes. We derive the broadcasting map that preserves the complex amplitude, while optimally reducing the noise in conjugate quadratures. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting). We prove similar results for purification (M<=N) and for phase-conjugate broadcasting.

Physical review, 2022

The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, probabilistically sending an unknown qubit state to two receivers, sending different qubit states to two receivers, and sending qutrit states to two receivers. Finally, we discuss some applications of these protocols.

Physical Review A, 2007

We address the problem of broadcasting N copies of a generic qubit state to M > N copies by estimating its direction and preparing a suitable output state according to the outcome of the estimate. This semiclassical broadcasting protocol is more restrictive than a general one, since it requires an intermediate step where classical information is extracted and processed. However, we prove that a suboptimal superbroadcasting, namely broadcasting with simultaneous purification of the local output states with respect to the input ones, is possible. We show that in the asymptotic limit of M → ∞ the purification rate converges to the optimal one, proving the conjecture that optimal broadcasting and state estimation are asymptotically equivalent. We also show that it is possible to achieve superbroadcasting with simultaneous inversion of the Bloch vector direction (universal NOT). We prove that in this case the semiclassical procedure of state estimation and preparation turns out to be optimal. We finally analyse semiclassical superbroadcasting in the phase-covariant case.

Arxiv preprint quant-ph/0603098, 2006

Abstract: We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for ...

Physical Review Letters, 1999

We introduce a new decomposition of the multiqubit states of the form ρ ⊗N and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state estimation of mixed states.

Europhysics Letters (EPL), 2006

We consider the problem of broadcasting arbitrary states of radiation modes from N to M > N copies by a map that preserves the average value of the field and optimally reduces the total noise in conjugate variables. For N ≥ 2 the broadcasting can be achieved perfectly, and for sufficiently noisy input states one can even purify the state while broadcasting-the socalled superbroadcasting. For purification (i.e. M ≤ N), the reduction of noise is independent of M. Similar results are proved for broadcasting with phase-conjugation. All the optimal maps can be implemented by linear optics and linear amplification.