Ultimate Limits for Multiple Quantum Channel Discrimination

Power of Sequential Protocols in Hidden Quantum Channel Discrimination

In many natural and engineered systems, unknown quantum channels act on a subsystem that cannot be directly controlled and measured, but is instead learned through a controllable subsystem that weakly interacts with it. We study quantum channel discrimination (QCD) under these restrictions, which we call hidden system QCD. We find sequential protocols achieve perfect discrimination and saturate the Heisenberg limit. In contrast, depth-1 parallel and multishot protocols cannot solve hidden system QCD. This suggests sequential protocols are superior in experimentally realistic situations.

Experimental Quantum Channel Discrimination Using Metastable States of a Trapped Ion

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped ^{40}Ca^{+} ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the six-dimensional D_{5/2} state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding 99% in each case, limited entirely by known experimental imperfections.

Quantum Readout of Imperfect Classical Data

The encoding of classical data in a physical support can be done up to some level of accuracy due to errors and the imperfection of the writing process. Moreover, some degradation of the stored data can happen over time because of physical or chemical instability of the system. Any readout strategy should take into account this natural degree of uncertainty and minimize its effect. An example are optical digital memories, where the information is encoded in two values of reflectance of a collection of cells. Quantum reading using entanglement, has been shown to enhances the readout of an ideal optical memory, where the two level are perfectly characterized. In this work, we analyse the case of imperfect construction of the memory and propose an optimized quantum sensing protocol to maximize the readout accuracy in presence of imprecise writing. The proposed strategy is feasible with current technology and is relatively robust to detection and optical losses. Beside optical memories, this work have implications for identification of pattern in biological system, in spectrophotometry, and whenever the information can be extracted from a transmission/reflection optical measurement.

Strict Hierarchy between Parallel, Sequential, and Indefinite-Causal-Order Strategies for Channel Discrimination

We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel discrimination that involve indefinite causal order and show that there exists a strict hierarchy among the performance of all four strategies. Our proof technique employs a general method of computer-assisted proofs. We also provide a systematic method for finding pairs of channels that showcase this phenomenon, demonstrating that the hierarchy between strategies is not exclusive to our main example.

Excluding false negative error in certification of quantum channels

Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false negative error after a finite number of queries in parallel, but cannot be distinguished unambiguously. Moreover, it will be proved that parallel certification scheme is always sufficient, however the number of steps may be decreased by the use of adaptive scheme. Finally, we consider examples of certification of various classes of quantum channels and measurements.

Bounding the Benefit of Adaptivity in Quantum Metrology Using the Relative Fidelity

Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this Letter, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimizing this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an N-use protocol is no more than N^{2} times the one-shot QFI.

Fundamental limitations on distillation of quantum channel resources

Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

Several key tasks in quantum information processing can be regarded as channel manipulation. Here, focusing on the class of distillation protocols, the authors derive general bounds on resource overhead and incurred errors, showing application to magic state distillation and quantum channel capacities.

Quantum Ranging with Gaussian Entanglement

It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination, when first proposed, was surprising as the entanglement's benefit survived entanglement-breaking noise. Since then, many efforts have been devoted to study quantum sensing in noisy scenarios. The applicability of such schemes, however, is limited to a binary quantum hypothesis testing scenario. In terms of target detection, such schemes interrogate a single spatiotemporal resolution bin at a time, limiting the impact to radar detection. We resolve this binary-hypothesis limitation by proposing an entanglement-assisted quantum ranging protocol. By formulating a ranging task as a multiary hypothesis testing problem, we show that entanglement enables a 6-dB advantage in the error exponent against the optimal classical scheme. Moreover, the proposed ranging protocol can also be used to implement a pulse-position modulated entanglement-assisted communication protocol. Our ranging protocol reveals entanglement's potential in general quantum hypothesis testing tasks and paves the way toward a quantum-ranging radar with a provable quantum advantage.

Simple Upper and Lower Bounds on the Ultimate Success Probability for Discriminating Arbitrary Finite-Dimensional Quantum Processes

We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of fundamental importance, but is challenging mainly due to the necessity of considering all discrimination strategies allowed by quantum mechanics, including entanglement-assisted strategies and adaptive strategies. In the case in which the processes to be discriminated have internal memories, the ultimate performance would generally be more difficult to analyze. In this Letter, we present a simple upper bound on the ultimate success probability for discriminating arbitrary quantum processes. In the special case of multishot channel discrimination, it can be shown that the ultimate success probability increases by at most a constant factor determined by the given channels if the number of channel evaluations increases by one. We also present a lower bound based on Bayesian updating, which has a low computational cost. Our numerical experiments demonstrate that the proposed bounds are reasonably tight. The proposed bounds do not explicitly depend on any quantum phenomena, and can be readily extended to a general operational probabilistic theory.

Experimental quantum reading with photon counting

The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading, this is achieved for information retrieval from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. We show, theoretically and experimentally, that quantum advantage is obtained by practical photon-counting measurements combined with a simple maximum-likelihood decision. In particular, we show that this receiver combined with an entangled two-mode squeezed vacuum source is able to outperform any strategy based on statistical mixtures of coherent states for the same mean number of input photons. Our experimental findings demonstrate that quantum entanglement and simple optics are able to enhance the readout of digital data, paving the way to real applications of quantum reading and with potential applications for any other model that is based on the binary discrimination of bosonic loss.