Isabel Sainz

Quantum error correction may delay, but also cause, entanglement sudden death

Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a states remaining entanglement.

Entanglement dynamics modified by an effective atomic environment

We study entanglement dynamics of a couple of two-level atoms resonantly interacting with a cavity mode and embedded in a dispersive atomic environment. We show that in the absence of the environment the entanglement reaches its maximum value when only one excitation is involved. Then, we find that the atomic environment modifies that entanglement dynamics and induces a typical collapse-revival structure even for an initial one photon Fock state of the field.

Unbiased nonorthogonal bases for tomographic reconstruction

We have developed a general method for constructing a set of nonorthogonal bases with equal separations between all different basis states in prime dimensions. The results are that the corresponding biorthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases, we derive an explicit expression for the optimal tomography in nonorthogonal bases. A special two-dimensional case is analyzed separately.

Quantum tomography via nonorthogonal basis and weak values

Using a relation between a biorthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases expansion.

Non-orthogonal Wigner-like mapping

We have developed a general method for construction of Wigner-like mapping to the phase-space associated with a non-orthogonal set of mutually unbiased equally separated bases. Explicit expressions of the Wigner functions in terms of measurements in non-orthogonal bases are given and the limit cases are analyzed.

Entanglement enhancement for two spins assisted by two phase kicks

We study the entanglement dynamics in a two-spin system governed by a bilinear Hamiltonian and assisted by phase kicks. It is found that the application of instant kicks to both spins at some specific moments leads to enhancement of entanglement. This procedure also improves the transient character of entanglement leading, for large spins, to a formation of a plateau for the I-concurrence. We have numerically investigated the spin-spin dynamics for several values of spins and observed a substantial enhancement of entanglement in comparison to the evolution without kicks.

COMBATING ENTANGLEMENT SUDDEN DEATH WITH NON-LOCAL QUANTUM-ERROR CORRECTION

We study the possibility of preventing finite-time disentanglement caused by dissipation by making use of non-local quantum error correction. This is made in comparison to previous results, where it was shown that local quantum error correction can delay disentanglement, but can also cause entanglement sudden death when it is not originally present.

Error estimation in the direct state tomography

We show that reformulating the Direct State Tomography (DST) protocol in terms of projections into a set of non-orthogonal bases one can perform an accuracy analysis of DST in a similar way as in the standard projection-based reconstruction schemes. i.e. in terms of the Hilbert-Schmidt distance between estimated and true states. This allows us to determine the estimation error for any measurement strength, including the weak measurement case, and to obtain an explicit analytic form for the average minimum square errors.

Detecting entanglement through correlations between local observables

We propose a measure of two-qubit entanglement that is invariant under local unitary transformations, and which is based on local measurements covariances. It measures the Hilbert-Schmidt distance ...

Estimating entanglement through local correlations

A bipartite, arbitrary-dimensional entanglement measure based on local correlations of any set of generators of the corresponding algebras is proposed. An explicit relation with the I- and 3-concurrences for pure states, and a limit for entangled mixed states, are given.