Mixed state discrimination using optimal control

Minimum-Consumption Discrimination of Quantum States via Globally Optimal Adaptive Measurements

Reducing the average resource consumption is the central quest in discriminating non-orthogonal quantum states for a fixed admissible error rate ϵ. The globally optimal fixed local projective measurement for this task is found to be different from that for previous minimum-error discrimination tasks [S. Slussarenko et al., Phys. Rev. Lett. 118, 030502 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.030502]. To achieve the ultimate minimum average consumption, here we develop a general globally optimal adaptive strategy (GOA) by subtly using the updated posterior probability, which works under any error rate requirements and any one-way measurement restrictions, and can be solved by a convergent iterative relation. First, under the local measurement restrictions, our GOA is solved to serve as the local bound, which saves 16.6 copies (24%) compared with the previously best globally optimal fixed local projective measurement. When the more powerful two-copy collective measurements are allowed, our GOA is experimentally demonstrated to beat the local bound by 3.9 copies (6.0%). By exploiting both adaptivity and collective measurements, our Letter marks an important step toward minimum-consumption quantum state discrimination.

Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy

The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We experimentally investigate the strategy for the optimal discrimination of two non-orthogonal states considering a fixed rate of inconclusive outcomes (FRIO). The main advantage of the FRIO strategy is to interpolate between unambiguous and minimum error discrimination by solely adjusting the rate of inconclusive outcomes. We present a versatile experimental scheme that performs the optimal FRIO measurement for any pair of generated non-orthogonal states with arbitrary a priori probabilities and any fixed rate of inconclusive outcomes. Considering different values of the free parameters in the FRIO protocol, we implement it upon qubit states encoded in the polarization mode of single photons generated in the spontaneous parametric down-conversion process. Moreover, we resort to a newfangled double-path Sagnac interferometer to perform a three-outcome non-projective measurement required for the discrimination task, showing excellent agreement with the theoretical prediction. This experiment provides a practical toolbox for a wide range of quantum state discrimination strategies using the FRIO scheme, which can significantly benefit quantum information applications and fundamental studies in quantum theory.

Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing

Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources and, thus, nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise. Unfortunately, an implementation of the optimum quantum receiver that would reap QI's full performance advantage has remained elusive, owing to its having to deal with a huge number of very noisy optical modes. We show how sum-frequency generation (SFG) can be fruitfully applied to optimum multimode Gaussian-mixed-state discrimination. Applied to QI, our analysis and numerical evaluations demonstrate that our SFG receiver saturates QI's quantum Chernoff bound. Moreover, augmenting our SFG receiver with a feedforward (FF) mechanism pushes its performance to the Helstrom bound in the limit of low signal brightness. The FF-SFG receiver, thus, opens the door to optimum quantum-enhanced imaging, radar detection, state and channel tomography, and communication in practical Gaussian-state situations.

Quantum State Discrimination Using the Minimum Average Number of Copies

In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the average error probability for fixed resources. Here we introduce a new state discrimination task: minimizing the average resources for a fixed admissible error probability. We show that this new task is not performed optimally by previously known strategies, and derive and experimentally test a detection scheme that performs better.

Minimum Copies of Schrödinger's Cat State in the Multi-Photon System

Multi-photon entanglement has been successfully studied by many theoretical and experimental groups. However, as the number of entangled photons increases, some problems are encountered, such as the exponential increase of time necessary to prepare the same number of copies of entangled states in experiment. In this paper, a new scheme is proposed based on the Lagrange multiplier and Feedback, which cuts down the required number of copies of Schrödinger's Cat state in multi-photon experiment, which is realized with some noise in actual measurements, and still keeps the standard deviation in the error of fidelity unchanged. It reduces about five percent of the measuring time of eight-photon Schrödinger's Cat state compared with the scheme used in the usual planning of actual measurements, and moreover it guarantees the same low error in fidelity. In addition, we also applied the same approach to the simulation of ten-photon entanglement, and we found that it reduces in priciple about twenty two percent of the required copies of Schrödinger's Cat state compared with the conventionally used scheme of the uniform distribution; yet the distribution of optimized copies of the ten-photon Schrödinger's Cat state gives better fidelity estimation than the uniform distribution for the same number of copies of the ten-photon Schrödinger's Cat state.

Null values and quantum state discrìmination

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

Guiding the time-evolution of a molecule: optical control by computer

The theory and computation of optical control has been developed over the last 25 years and is now a mature field of research. Initial work provided pictures of how control using light fields in simple systems may be achieved, for example using multiple excitation pathways or pulse sequences. The development of optimal control theory then provided a general method for guiding a system to its target using a shaped laser pulse. Combined with quantum dynamics simulations this has become a widely used tool, and has been applied to a range of systems to show what can be controlled. The present challenge is to gain more insight into the mechanism of control. In addition, methods need to be extended to reach the size of system of interest to technology. In this perspective article we shall give a brief overview of present capabilities and some of the recent developments in quantum dynamics and control simulations.

Local discrimination of mixed States

We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by local operations assisted with classical communication (LOCC). In contrast with the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former can require up to twice the number of copies of the latter. Our techniques can be used to bound the power of LOCC strategies in other similar settings, which is still one of the most elusive questions in quantum communication.

Determination of maximal Gaussian entanglement achievable by feedback-controlled dynamics

We determine a general upper bound for the steady-state entanglement achievable by continuous feedback for a system of any number of bosonic degrees of freedom. We apply such a bound to the specific case of parametric interactions--the most common practical way to generate entanglement in quantum optics--and single out optimal feedback strategies that achieve the maximal entanglement. We also consider the case of feedback schemes entirely restricted to local operations and compare their performance to the optimal, generally nonlocal, schemes.

Experimental feedback control of quantum systems using weak measurements

A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the disturbance they suffer in the process of measurement. In the context of a simple quantum control scenario-the stabilization of nonorthogonal states of a qubit against dephasing-we experimentally explore the use of weak measurements in feedback control. We find that, despite the intrinsic difficultly of implementing them, weak measurements allow us to control the qubit better in practice than is even theoretically possible without them. Our work shows that these more general quantum measurements can play an important role for feedback control of quantum systems.