Experimental Detection of Quantum Channel Capacities

Abstract

We present an efficient experimental procedure that certifies nonvanishing quantum capacities for qubit noisy channels. Our method is based on the use of a fixed bipartite entangled state, where the system qubit is sent to the channel input. A particular set of local measurements is performed at the channel output and the ancilla qubit mode, obtaining lower bounds to the quantum capacities for any unknown channel with no need of quantum process tomography. The entangled qubits have a Bell state configuration and are encoded in photon polarization. The lower bounds are found by estimating the Shannon and von Neumann entropies at the output using an optimized basis, whose statistics is obtained by measuring only the three observables σ_{x}⊗σ_{x}, σ_{y}⊗σ_{y}, and σ_{z}⊗σ_{z}.

Generation of quantum states with nonlinear squeezing by Kerr nonlinearity

“…Let us now move towards generating states with the nonlinear squeezing. At first we consider states with cubic nonlinearity [15,18,29,63]. Such states can be, in the idealized scenario, generated by applying a unitary cubic nonlinear operation given by Hamiltonian Ĥ = p3 onto a Gaussian squeezed state.…”

“…These can be the modes of optical [11][12][13] or microwave fields [14,15], or the vibrational modes of mechanical oscillators [16]. Alternatively they can be also systems of qubits of such a large number that their collective behavior is essentially continuous, such as in the case of collective magnetic spins [17,18]. Universal processing of continuous variable (CV) systems is defined as the ability to implement an arbitrary quantum operation [19].…”

“…The unitary operation with the lowest order of a nonlinearity sufficient for the universal processing is the cubic phase gate [23]. In some systems the gate can be implemented by a direct dynamical control of the system's parameters [15,18,24], but it can be universally realized through a measurement induced scheme [25][26][27][28] with help of suitably prepared ancillary states.…”

Convex approximations of quantum channels

“…This approach clearly has an immediate experimental application, especially when the quantum operations effectively feasible in a lab are limited due to intrinsic restrictions, unavailable technology, or even economic reasons. Further relevance of this approach is due to the fact that a convex sum of quantum channels offers the possibility of performing different experiments followed by post-processing of experimental data [11,12], when the quantities of interest are linear with respect to quantum operations.…”

Experimental transmission of quantum information using a superposition of causal orders

“…4 (b), where the orders of two identical copies of a completely depolarizing channel (DC) are combined coherently. Regarding quantum capacity Q [23][24][25][26], however, the enhancement is much more obscure, because no quantum information can be transmitted through the selfswitched channel [16]. Fortunately, we discovered that this advantage could be revealed by designing a conditional quan- tum channel (CQC) [27,28] (see Fig.…”