Abstract In this paper, we mainly study the indistinguishability of classically simulable measurements (measurements that can be effectively simulated on classical computers) in the tasks of quantum channel discrimination. First, we investigate the limitations of classically simulable measurements under unambiguous and perfect discrimination strategies. For unambiguous discrimination, we establish a conditional limitation result for channel-induced output-state discrimination scenarios, while for perfect discrimination we derive a sufficient condition under which classically simulable measurements fail to perfectly distinguish quantum channels. When considering the minimum-error discrimination strategy, we formulate the corresponding bilinear optimization problem and discuss its formal Lagrange dual formulation. Subsequently, we give the lower bound of the minimum-error probability obtained by using classically simulable measurements in the minimum-error discrimination task under the adaptive protocol. Furthermore, we give two measures of the nonstabilizerness (magic) of measurements. We prove that one measure we proposed can be used as an exact quantifier for the advantage in some tasks of quantum state discrimination. Finally, we investigate the relationship between classically simulable measurements and the data hiding ratio.
Abstract In this paper, we mainly study the indistinguishability of classically simulable measurements (measurements that can be effectively simulated on classical computers) in the tasks of quantum channel discrimination. First, we investigate the limitations of classically simulable measurements under unambiguous and perfect discrimination strategies. For unambiguous discrimination, we establish a conditional limitation result for channel-induced output-state discrimination scenarios, while for perfect discrimination we derive a sufficient condition under which classically simulable measurements fail to perfectly distinguish quantum channels. When considering the minimum-error discrimination strategy, we formulate the corresponding bilinear optimization problem and discuss its formal Lagrange dual formulation. Subsequently, we give the lower bound of the minimum-error probability obtained by using classically simulable measurements in the minimum-error discrimination task under the adaptive protocol. Furthermore, we give two measures of the nonstabilizerness (magic) of measurements. We prove that one measure we proposed can be used as an exact quantifier for the advantage in some tasks of quantum state discrimination. Finally, we investigate the relationship between classically simulable measurements and the data hiding ratio.
Quantum hypothesis testing is an important tool for quantum information processing.Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained.In both scenarios, the testing between quantum states is relatively well understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood.Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown.In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels.In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols.For the special class of "teleportation-covariant" channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.
Classically simulable measurements (CSMs) constitute an important class of restricted measurements in the odd-prime-dimensional magic resource theory, referring to those measurements with positive discrete Wigner functions. Since their discrimination power is weaker than that of global measurements, it is necessary to study how to improve the discrimination power of CSMs. In this paper, we consider three methods to improve the discrimination power of CSMs, including adding magic resources, using quantum catalysts, and using quantum memories. Specifically, we relate measurements with positive discrete Wigner functions to completely positive Wigner-preserving measurement channels, thereby transforming the problem of improving the discrimination power of CSMs into the problem of determining how many magic resources are required to simulate quantum channels using free operations. Based on this, we derive the lower and upper bounds of the simulation cost. Moreover, we provide a concrete example for which these bounds coincide and prove that consumable magic resources can enhance the discrimination power of CSMs. Finally, we establish a no-go theorem, which shows that for discriminating a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination using CSMs.
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for a revised unambiguous discrimination task in the unasymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical unambiguous discrimination, we show the advantage of the quantum by considering a quantifier on a set of semidefinite positive operators.
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider an extended unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for an extended unambiguous discrimination task in the non-asymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical generalized unambiguous discrimination, we show the advantage of the quantum with the aid of a quantifier based on a set of semi-definite positive operators.
Abstract What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation.
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial ``no-measurement'' strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.