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We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider the so-called constant-$\hat{p}$ displaced states which include mixtures of multimode coherent states arbitrarily displaced along a common axis. We first show that no global or local Gaussian transformations or generalized Gaussian measurements can lead to a better discrimination method than simple homodyne measurements applied to each mode separately and classical postprocessing of the results. This result is applied to binary state comparison problems. We show that homodyne measurements, separately performed on each mode, are the best Gaussian measurement for binary state comparison. We further compare the performance of the optimal Gaussian strategy for binary coherent states comparison with these of non-Gaussian strategies using photon detections., 8 pages, 3 figures

Networking is integral to quantum communications1 and has significant potential for upscaling quantum computer technologies2. Recently, it was realized that the sensing performances of multiple spatially distributed parameters may also be enhanced through the use of an entangled quantum network3–10. Here, we experimentally demonstrate how sensing of an averaged phase shift among four distributed nodes benefits from an entangled quantum network. Using a four-mode entangled continuous-variable state, we demonstrate deterministic quantum phase sensing with a precision beyond what is attainable with separable probes. The techniques behind this result can have direct applications in a number of areas ranging from molecular tracking to quantum networks of atomic clocks. Experiments demonstrate quantum phase sensing with a four-mode entangled state, reaching a measurement precision that is beyond what can be achieved by separate individual probes.

One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exist. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto an arbitrary superposition of two weak coherent states in optical system. The measurement operators are reconstructed experimentally by a novel quantum detector tomography protocol. Our device is realized by combining the displacement operation and photon counting, well established technologies, and thus has implications in various optical quantum information processing applications.

In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put vacuum into one input port of a balanced Mach-Zehnder Interferometer, then no matter what you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the shot noise limit (SNL). Often the proof of this theorem is cited to be in Ref. [C. Caves, Phys. Rev. D 23, 1693 (1981)], but upon further inspection, no such claim is made there. A quantum-Fisher-information-based argument suggestive of this no-go theorem appears in Ref. [M. Lang and C. Caves, Phys. Rev. Lett. 111, 173601 (2013)], but is not stated in its full generality. Here we thoroughly explore this no-go theorem and give the rigorous statement: the no-go theorem holds whenever the unknown phase shift is split between both arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications., 9 pages, 2 figures

We consider the phase sensing via a weak optical coherent state at quantum limit precision. A detection scheme for the phase estimation is proposed, which is inspired by the suboptimal quantum measurement in coherent optical communication. We theoretically analyze a performance of our detection scheme, which we call the displaced-photon counting, for phase sensing in terms of the Fisher information and show that the displaced-photon counting outperforms the static homodyne and heterodyne detections in a wide range of the target phase. The proof-of-principle experiment is performed with linear optics and a superconducting nanowire single-photon detector. The result shows that our scheme overcomes the limit of the ideal homodyne measurement, even under practical imperfections.

The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off--type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.

Generalized quantum measurements identifying nonorthogonal states without ambiguity often play an indispensable role in various quantum applications. For such an unambiguous state-discrimination scenario, we have a finite probability of obtaining inconclusive results and minimizing the probability of inconclusive results is of particular importance. In this paper, we experimentally demonstrate an adaptive generalized measurement that can unambiguously discriminate the quaternary phase-shift-keying coherent states with a near-optimal performance. Our scheme is composed of displacement operations, single-photon detections and adaptive control of the displacements dependent on a history of photon-detection outcomes. Our experimental results show a clear improvement of both a probability of conclusive results and a ratio of erroneous decision caused by unavoidable experimental imperfections over conventional static generalized measurements.POPULAR SUMMARYIn our everyday life, we are usually able to tell two similar but different things apart by choosing the right way of observing them. Even “identical” twins will have different personalities or perhaps birthmarks in different places. This is no longer the case when looking at quantum objects. Quantum states that are nonorthogonal, i.e., have a certain overlap, cannot be perfectly distinguished, no matter what measurement you attempt. This is a central property of quantum mechanics.Quantum state discrimination is the task of figuring out which quantum state you have at hand, typically out of a small set of candidates. When you cannot distinguish the states perfectly, you will need to decide what to give up on: You can give up trying to know for certain which state you have. Alternatively, you can give up trying to get a conclusive answer every time. Depending on what you are trying to accomplish, either of those strategies may be advantageous.In this work, we study the latter approach, unambiguous state discrimination in the technologically relevant context of distinguishing four very weak laser pulses with distinct phases. We introduce and demonstrate a measurement scheme, based on photon detection and fast feedback to the laser pulse, which significantly improves on the best existing schemes. We obtain near-optimal probabilities of obtaining a conclusive answer and low error probabilities. We expect that quantum key distribution as well as classical optical communication, which is ultimately limited by quantum noise, may benefit from our newly developed technique.