Experimental observations are usually described using theoretical models that make assumptions about the dimensionality of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness 1-6 answers this question, as it allows bounding the dimension of an unknown system only from measurement statistics. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario 6 . We use photon pairs entangled in polarization and orbital angular momentum 7-9 to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our work opens new avenues in quantum information science, where dimension represents a powerful resource 10-12 , especially for device-independent estimation of quantum systems 13-16 and quantum communications 17,18 .Dimensionality is one of the most basic and essential concepts in science, inherent to any theory aiming at explaining and predicting experimental observations. In building up a theoretical model, one makes some general and plausible assumptions about the nature and the behaviour of the system under study. The dimension of this system, that is, the number of relevant and independent degrees of freedom needed to describe it, represents one of these initial assumptions. In general, the failure of a theoretical model in predicting experimental data does not necessarily imply that the assumption on the dimensionality is incorrect, because there might exist a different model assuming the same dimension that is able to reproduce the observed data.A natural question is whether this approach can be reversed and whether the dimension of an unknown system, classical or quantum, can be estimated experimentally. Clearly, the best one can hope for is to provide lower bounds on this unknown dimension. Indeed, every physical system has potentially an infinite number of degrees of freedom, and one can never exclude that they are all necessary to describe the system in more complex experimental arrangements. The goal, then, is to obtain a lower bound on the dimension of the unknown system from the observed measurement data without making any assumption about the detailed functioning of the devices used in the experiment. Besides its fundamental interest, estimating the dimension of an unknown quantum system is also relevant from the perspective of quantum information science, where the Hilbert space dimension is considered as a resource. For instance, using higher-dimensional Hilbert spaces simplifies quantum logic for quantum computation 10 , enables the optimal realization of information-theoretic protocols 11,19,20 and allows for lower detection efficiencies in Bell experiments 21,22 . Moreover, the dimension of quantum systems plays a crucial role in security proofs of standard quantum...
We report on the experimental verification of quantum non-Gaussian character of a heralded single-photon state with a positive Wigner function. We unambiguously demonstrate that the generated state cannot be expressed as a mixture of Gaussian states. Sufficient information to witness the quantum non-Gaussian character is obtained from a standard photon anticorrelation measurement.
We propose a protocol for conditional suppression of losses in direct quantum state transmission over a lossy quantum channel. The method works by noiselessly attenuating the input state prior to transmission through a lossy channel followed by noiseless amplification of the output state. The procedure does not add any noise hence it keeps quantum coherence. We experimentally demonstrate it in the subspace spanned by vacuum and single-photon states, and consider its general applicability.PACS numbers: 03.67. Hk, 42.50.Ex Quantum communication holds the promise of unconditionally secure information transmission [1]. However, the distance over which quantum states of light can be distributed without significant disturbance is limited due to unavoidable losses and noise in optical links. Losses, as well as errors or decoherence, may in principle be overcome by the sophisticated techniques of quantum error correction [2][3][4], entanglement distillation [5][6][7], and quantum repeaters [8,9]. However, these techniques typically require encoding information into complex multimode entangled states, processing many copies of an entangled state, and -even more challenging -using quantum memories [10,11]. In stark contrast with the situation for classical communication, losses in quantum communication cannot be compensated by amplifying the signal, because the laws of quantum mechanics imply that any deterministic phase-insensitive signal amplification is unavoidably accompanied by the addition of noise [12].Very recently, however, the concept of heralded noiseless amplification of light [13] was proposed as a way out, relaxing the deterministic requirement. The noiseless amplification is formally described by a quantum filter g n , where n is the photon number operator and g > 1 denotes the amplification gain. The noiseless amplifier thus modulates amplitudes of Fock states |n by factor g n . This filtration can conditionally increase amplitude of a coherent state |α without adding any noise, g n |α ∝ |gα . Although this cannot be done perfectly because g n is unbounded, faithful noiseless amplification is possible in any finite subspace spanned by the Fock states |n with n ≤ N , albeit with a correspondingly low probability scaling as g −2N in the worst case of input vacuum state. With current technology, it has been proven possible to faithfully noiselessly amplify weak coherent states containing mostly vacuum and single-photon contributions [14][15][16][17].The noiseless amplifier can improve the performance of quantum key distribution protocols [18][19][20][21] and it can also be used to distribute high-quality entanglement over a lossy channel [13,22]. Beyond that, the noiseless amplifier is not useful to suppress losses in direct transmission of arbitrary quantum states because it is not the inverse map of a lossy channel L. As a matter of fact, any superposition of Fock states that is not a coherent state is mapped by L onto a mixed state, and this added noise cannot be eliminated by noiseless amplification.He...
We introduce and experimentally explore the concept of the non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly witnessed quantum non-Gaussianity withstands significant attenuation, exhibiting a depth of 18 dB, while the nonclassicality remains unchanged. Quantum non-Gaussian depth is an experimentally approachable quantity that is much more robust than the negativity of the Wigner function. Furthermore, we use it to reveal significant differences between otherwise strongly nonclassical single-photon sources.
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