Quantum Benchmark Research Articles

Quantum benchmarking with realistic states of light

The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the test states used in quantum benchmarking experiments may be imperfect as well. Many quantum benchmarks are only valid for states which match some ideal form, such as pure states or Gaussian states. We outline how to perform quantum benchmarking using arbitrary states of light. We demonstrate these results using real data taken from a continuous-variable quantum memory.

Schmidt-number benchmark for genuine quantum memories and gates

We propose to apply the notion of the Schmidt number in order to show that a quantum memory or gate process is capable of maintaining a genuine multi-level quantum coherence. We present a simple criterion in terms of an average gate fidelity with respect to the input states of two mutually unbiased bases and demonstrate the coherence of the gate operation in several existing experiments. The Schmidt-number benchmark naturally includes the quantum benchmark as a specific case.

Strong quantitative benchmarking of quantum optical devices

Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify such devices retain their quantum advantages. Benchmarks based on witnessing entanglement have proven useful for verifying the true quantum nature of these devices. The next challenge is to characterize how strongly a device is within the quantum domain. We present a method, based on entanglement measures and rigorous state truncation, which allows us to characterize the degree of quantumness of optical devices. This method serves as a quantitative extension to a large class of previously-known quantum benchmarks, requiring no additional information beyond what is already used for the non-quantitative benchmarks.

Simple proof of the quantum benchmark fidelity for continuous-variable quantum devices

An experimental success criterion for continuous-variable quantum teleportation and memories is to surpass a limit of the average fidelity achieved by the classical measure-and-prepare schemes with respect to a Gaussian distributed set of coherent states. We present a simple proof of the classical limit based on the familiar notions of the state-channel duality and the partial transposition. The present method enables us to produce a quantum-domain criterion associated with a given set of measured fidelities.

Quantum benchmarks for the storage or transmission of quantum light from minimal resources

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.

Phase-covariant quantum benchmarks

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.

Alternative fidelity measure between quantum states

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa's axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states

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 , 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.

Publisher’s Note: Quantum Benchmark for Teleportation and Storage of Squeezed States [Phys. Rev. Lett.100, 170503 (2008)

Received 30 April 2008DOI:https://doi.org/10.1103/PhysRevLett.100.189902©2008 American Physical Society

Quantum Benchmark for Teleportation and Storage of Squeezed States

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.

Quantum Benchmark for Storage and Transmission of Coherent States

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.

Parallel computing in quantum chemistry — Message passing and beyond for a general ab initio program system

The parallelization of the diagonalization step of the COLUMBUS MRSDCI program system is reported. A coarse grain algorithm has been developed by means of a segmentation of the trial and resulting update vectors of the iterative Davidson scheme. Message passing based on the TCGMSG toolkit and the global array (GA) tools are used. The latter program system allows an asynchronous access to data structures in the spirit of shared memory. The importance of portable facilities like GA going beyond message passing is stressed for quantum chemical methods and benchmark result for the Intel Touchstone Delta are given.