We give a quantum benchmark for teleportation and quantum storage experiments suited for pure and mixed test states. The benchmark is based on the average fidelity over a family of phase-covariant states and certifies that an experiment cannot be emulated by a classical setup, i.e., by a measure-and-prepare scheme. We give an analytical solution for qubits, which shows important differences with standard state estimation approach, and compute the value of the benchmark for coherent and squeezed states, both pure and mixed.
We give a quantum benchmark for teleportation and quantum storage experiments suited for pure and mixed test states. The benchmark is based on the average fidelity over a family of phase-covariant states and certifies that an experiment cannot be emulated by a classical setup, i.e., by a measure-and-prepare scheme. We give an analytical solution for qubits, which shows important differences with standard state estimation approach, and compute the value of the benchmark for coherent and squeezed states, both pure and mixed.
In this thesis I study optimal strategies to estimate or characterize quantum states and processes (quantum channels). I consider the problem of estimating a phase encoded on a gaussian state. Phase estimation is at the heart of many quantum metrology applications, such as gravitational wave detectors or clock synchronization. I address the problem to the phase estimation fidelity for pure and mixed gaussian states and study how temperature affects the precision of estimation. Although the case of pure states has been studied before, very little is known about estimation in mixed states. The interest in mixed gaussian states relies on the fact that these are the states one has in real experiments with light due to the unavoidable presence of noise. Displaced and squeezed thermal states are studied. For the case of displaced states, I find that fidelity estimation gets worse when the temperature increases. On the contrary, for squeezed thermal states I find the surprising result that a larger temperature yields better estimation. This apparently paradoxical feature, also appears when I derive the estimation accuracy that can be obtained when an asymptotically large number of copies of the state is available. I also study quantum benchmarks that can be applied to a wide variety of protocols, such us quantum storage or quantum teleportation. A very important question in QIT is to know whether a particular quantum protocol can be realized by classical means with the same efficiency. After all, QIT lives from the promise of this quantum advantage. This question becomes specially relevant in experimental (real) implementations of quantum schemes. In real experiments there are always losses and the ideal quantum protocols become imperfect. It is then necessary to assess whether the same experimental result could be obtained by classical (less costly) means. So, for example, in a particular teleportation experiment -which involves generation of entanglement, complicated Bell measurements, fighting decoherence, etc.- one might ask whether one could achieve the same (i.e. mapping the state of a system to a second system located in a different place or time) by measuring the system, transmitting the collected information to the other location, and finally preparing the system accordingly. It is hence of paramount importance to give bounds on the efficiency of these measure and prepare (or entanglement breaking) channels. For this purpose we propose a threshold based on a phase-covariant family of states. Besides of being a family with a straightforward group-theoretical structure, which gives obvious computational advantages, this family is interesting because it can be tested experimentally also in a straightforward way. A crucial feature for the practical use of our benchmark is that it does not require pure (ideal) input states. I finally consider the problem of estimating the parameter of the amplification channel. The amplification channel is interesting by itself but also by the fact that the Hawking-Unruh effect can be formally modeled by it. The Unruh-Hawking effect is a relativistic effect and as such it is hard to measure and detect in current experiments. I investigate whether quantum strategies can provide an improvement over classical protocols in the estimation of the amplification parameter. If the field is inertially prepared in the vacuum one could measure its temperature as detected by a noninertial observer and extract information about the parameter. But I would like to know if the vacuum state is the optimal probe state in an inertial frame for such a task or a better sensitivity could be achieved if the field were in a state of nonzero energy (mean photon number) from an inertial perspective. The aim is to determine the optimal input states, so that, by optimally measuring the output, one can construct an estimator for amplification channel parameter which is unbiased and has the minimum possible variance.
Quantum benchmarks are routinely used to validate the experimental demonstration of quantum information protocols. Many relevant protocols, however, involve an infinite set of input states, of which only a finite subset can be used to test the quality of the implementation. This is a problem, because the benchmark for the finitely many states used in the test can be higher than the original benchmark calculated for infinitely many states. This situation arises in the teleportation and storage of coherent states, for which the benchmark of 50% fidelity is commonly used in experiments, although finite sets of coherent states normally lead to higher benchmarks. Here, we show that the average fidelity over all coherent states can be indirectly probed with a single setup, requiring only two-mode squeezing, a 50-50 beam splitter, and homodyne detection. Our setup enables a rigorous experimental validation of quantum teleportation, storage, amplification, attenuation, and purification of noisy coherent states. More generally, we prove that every quantum benchmark can be tested by preparing a single entangled state and measuring a single observable.
We provide a quantum benchmark for teleportation and storage of single-mode squeezed states with zero displacement and a completely unknown degree of squeezing along a given direction. For pure squeezed input states, a fidelity higher than 81.5% has to be attained in order to outperform any classical strategy based on an estimation of the unknown squeezing and repreparation of squeezed states. For squeezed thermal input states, we derive an upper and a lower bound on the classical average fidelity which tighten for moderate degree of mixedness. These results enable a critical discussion of recent experiments with squeezed light.
Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.
Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large-scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.
We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing s is fixed, no information about its orientation in phase space is given, and the distribution of phase space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for s=1) is given by s/(1+s), vanishing when the degree of squeezing diverges. For mixed states, as well as for general distributions of displacements, we reduce the determination of the benchmarks to the solution of a finite-dimensional semidefinite program, which yields accurate, certifiable bounds thanks to a rigorous analysis of the truncation error. This approach may be easily adapted to more general ensembles of input states.