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Register a new userWitnesses of coherence and dimension from multiphoton indistinguishability tests
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Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric set-up to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests. Besides coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness. Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.
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We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses $W_1, W_2, cdots, W_n$ can detect some common coherent states if and only if $sum_{i=1}^nt_iW_i$ is still a witnesses for any nonnegative numbers $t_i(i=1,2,cdots,n)$. We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Here we show that so-called Sylvester interferometers are near-optimal for the task of discriminating the behaviors of distinguishable and indistinguishable photons. We report the first implementations of integrated Sylvester interferometers with 4 and 8 modes with an efficient, scalable and reliable 3D-architecture. We perform two-photon interference experiments capable of identifying indistinguishable photon behaviour with a Bayesian approach using very small data sets. Furthermore, we employ experimentally this new device for the assessment of scattershot Boson Sampling. These results open the way to the application of Sylvester interferometers for the optimal assessment of multiphoton interference experiments.
We show that temporal two-photon interference effects involving the signal and idler photons created by parametric down-conversion can be fully characterized in terms of the variations of two length parameters--called the biphoton path-length difference and the biphoton path-asymmetry- length difference--which we construct using the six different length parameters that a general two-photon interference experiment involves. We perform an experiment in which the effects of the variations of these two parameters can be independently controlled and studied. In our experimental setup, which does not involve mixing of signal and idler photons at a beam splitter, we further report observations of Hong-Ou-Mandel- (HOM-)like effects both in coincidence and in one-photon count rates. As an important consequence, we argue that the HOM and the HOM-like effects are best described as observations of how two-photon coherence changes as a function of the biphoton path- asymmetry-length difference.
For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses, or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.
In the present work, the effect of resonant pumping schemes in improving the photon coherence is investigated on InAs/InGaAs/GaAs quantum dots emitting in the telecom C-band. The linewidths of transitions of multiple exemplary quantum dots are determined under above-band pumping and resonance fluorescence via Fourier-transform spectroscopy and resonance scans, respectively. The average linewidth is reduced from $9.74,mathrm{GHz}$ in above-band excitation to $3.50,mathrm{GHz}$ in resonance fluorescence underlining its superior coherence properties. Furthermore, the feasibility of coherent state preparation with a fidelity of $49.2,%$ is demonstrated, constituting a step towards on-demand generation of coherent, single C-band photons from quantum dots. Finally, two-photon excitation of the biexciton is investigated as a resonant pumping scheme. A deconvoluted single-photon purity value of $g^{(2)}_{mathrm{HBT}}(0)=0.072pm 0.104$ and a degree of indistinguishability of $V_{mathrm{HOM}}=0.894pm0.109$ are determined for the biexciton transition. This represents an important step towards fulfilling the prerequisites for quantum communication applications like quantum repeater schemes at telecom wavelength.
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