We investigate several recently published benchmark criteria for storage or transmission of quantum information. A comparison reveals that criteria based on a Gaussian distribution of coherent states are most resilient to noise. We then address the issue of experimental resources and derive an equally strong benchmark, solely based on three coherent states and homodyne detection. This benchmark is further simplified in the presence of naturally occurring random phases, which remove the need for active input state modulation.
We investigate several recently published benchmark criteria for storage or transmission of quantum information. A comparison reveals that criteria based on a Gaussian distribution of coherent states are most resilient to noise. We then address the issue of experimental resources and derive an equally strong benchmark, solely based on three coherent states and homodyne detection. This benchmark is further simplified in the presence of naturally occurring random phases, which remove the need for active input state modulation.
We investigate several recently published benchmark criteria for storage or transmission of continuous-variable quantum information. A comparison reveals that criteria based on a Gaussian distribution of coherent states are most resilient to noise. We then address the issue of experimental resources and derive an equally strong benchmark, solely based on three coherent states and homodyne detection. This benchmark is further simplified in the presence of naturally occurring random phases, which remove the need for active input-state modulation.
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.
Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous-variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.
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 consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.
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.