Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit

TLDR: In this article, a reconfigurable integrated quantum photonic circuit consisting of a two-qubit entangling gate, several Hadamard-like gates and eight variable phase shifters is presented.

Abstract: Researchers demonstrate a reconfigurable integrated quantum photonic circuit. The device comprises a two-qubit entangling gate, several Hadamard-like gates and eight variable phase shifters. The set-up is used to generate entangled states, violate a Bell-type inequality with a continuum of partially entangled states and demonstrate the generation of arbitrary one-qubit mixed states.

Figures

FIG. 1: A two-photon reconfigurable quantum circuit for generating, manipulating and detecting entanglement and mixture. a Quantum circuit diagram consisting of pairs of Hadamard-like gates H ′ = eiπ/2e−iπσZ/4He−iπσZ/4 (where H is the usual Hadamard gate) and Rz(φ) = e −iφσz/2 rotations, that together implement Ûi,f (φj , φk), and two H ′ gates and a controlled-sign or cz gate, that together implement a cnot. b Waveguide implementation of the circuit composed of directional couplers and voltage controlled thermo-optic phase shifters drawn as orange triangles. Directional couplers with splitting ratio η = 1/3 are marked with a dot, all other couplers have η = 1/2.

FIG. 2: Classical and quantum interference fringes. a Interference fringe measured at the two outputs of a single Mach-Zehnder (MZ) interferometer on the chip. Experimental data are presented as black circles. Solid lines show fits. b Hong-Ou-Mandel dip, measured using a single MZ interferometer as a beamsplitter. Two-photon coincidence counts are shown as black circles. The red line shows a fit to this data with Gaussian and sinc components, due to quantum interference and determined by the spectral filters used, and a linear term accounting for slight decoupling of the source. The blue line shows a fit to the measured rate of accidental coincidences, with Gaussian and linear components. Error bars in both figures assume Poissonian statistics.

FIG. 3: Statistical fidelity of photon . The histogram shows the distribution of statistical fidelity between ideal and measured coincidence probabilities, over 995 sets of eight randomly selected phases ϕ̃. 96% of phase settings produced statistics corresponding with theory to f > 0.97.

FIG. 5: CHSH manifold. a The Bell-CHSH sum S, plotted as a function of phases α and β. In the α axis, the state shared between Alice and Bob is tuned continuously between product states at α = 0, π and maximally entangled states at α = π/2, 3π/2. The β axis shows S as a function of Bob’s variable measurements, which can be thought of as two operator-axes in the real plane of the Bloch sphere, fixed with respect to each other at an angle of π/2 but otherwise free to rotate with angle β between 0 and 2π. The blue curves show a projection of the manifold onto each axis. Yellow contours mark the edges of regions of the manifold which violate −2 ≤ S ≤ 2. Red lines on the axes also show this limit. b Experimentally measured manifold. Data points are drawn as black circles. Data points which violate the CHSH inequality are drawn as yellow circles. The surface shows a fit to the experimental data.

FIG. 6: Histogram showing the statistical distribution of quantum state fidelity between 119 randomly chosen singlequbit target states and the corresponding mixed states generated and characterized on-chip. Inset: Ψ drawn in the Bloch sphere using 63 mixed states, again generated and characterized on-chip. These states are chosen from the real plane of the sphere for clarity. Note that each point is derived from a different bipartite partially entangled state.

Frequently asked questions

Q1. How was the phase in the interferometer measured?

1. The phase in the interferometer was then set to π/2, rendering it equivalent to a 1/2 reflectivity beamsplitter, and the two-photon coincidence count N across the outputs of the interferometer was measured as a function of an off-chip optical delay between the arrival times of the two photons. 

Q2. How many measurements were needed to reconstruct the density operator of the state?

The authors used the arbitrary single-qubit measurement capability of the circuit to perform maximum-likelihood quantum state tomography (QST)25 on these four states: phase shifters φ5−8 were used to implement each of the 16 measurements necessary to reconstruct the density operator of the state. 

Q3. How many photons were collected from the output of the chip?

Photons were collected from the output of the chip also using arrays of polarisation maintaining fibre and detected with fibre coupled SPCMs. 

Q4. What is the fidelity of the state of the entanglement approach?

High fidelity production and measurement of states of arbi-5trary entanglement and mixture will be essential for characterisation of quantum devices, and will provide a reliable means to test the unique properties of quantum physics. 

Q5. What is the implication of the formalism of quantum mechanics?

Entangled states of quantum systems are the fundamental resource in quantum information and represent the most nonclassical implication of the formalism of quantum mechanics. 

Q6. How many states can be generated in the reduced density matrix?

By choosing α, β, γ, δ, via setting φ1−4, the amount of mixture in this reduced density matrix can be continuously varied between 0 and 1. 

Q7. How did the authors characterise the quantum circuit?

Having observed high-fidelity classical and quantum interference at individual MZ interferometers on the chip, the authors then used a stochastic method to characterise the operational performance of the quantum circuit as a whole, across the full space of possible configurations. 

Q8. What could be used to manipulate hyper-entanglement?

Circuits such as the one presented here could be used in conjunction with adaptive (classical) algorithms to bypass the need for calibration of the phase shifters in particular applications. 

Q9. What was the cladding of the waveguides?

The waveguide device was fabricated on a silicon wafer, upon which a 16µm layer of undoped silica was deposited to form the lower cladding of the waveguides. 

Q10. How many phase shifters are used in the circuit?

In order to characterize the precision and accuracy with which the device can be reconfigured the authors injected single photons into the device via a polarization maintaining optical fibre array, and measured interference fringes across each of the eight phase shifters on the chip, finding an average contrast C = 0.988 ± 0.008. 

Q11. What are the main sponsors of this work?

This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), the European Research Council (ERC), Intelligence Advanced Research Projects Activity (IARPA), the Leverhulme Trust, the Centre for Nanoscience and Quantum Information (NSQI), PHORBITECH, the Quantum Information Processing Interdisciplinary Research Collaboration (QIP IRC), and the Quantum Integrated Photonics (QUANTIP) project. 

Q12. What is the advantage of using the entanglement approach in practical applications?

6. An advantage of using the entanglement approach in practical applications is that it does not require pseudo/quantum-random number generators. 

Q13. What is the cnot gate in the middle of the circuit shown in Fig. 1?

In addition to high-fidelity classical interference, as demonstrated in Fig. 2a, the cnot gate in the middle of the circuit shown in Fig 1 relies on high-fidelity quantum interference16. 

Q14. How many states have fidelity above 0.95?

The average quantum state fidelity across all 119 states was measured to be 0.98±0.02, with 91% of states having fidelity > 0.95. 

Q15. What is the simplest way to achieve a two-photon coincidence count?

Typical two-photon coincidence count rates of 100kHz were achieved using ∼ 60% efficient, silicon based avalanche photo-diode single photon counting modules (SPCM). 

Q16. How did the authors produce degenerate photon pairs?

The authors produced degenerate photon pairs, sharing the same spectral and polarization mode, via type-I spontaneous parametric downconversion23 (see Methods) which were injected into the chip as shown in Fig. 

Q17. What is the probability-theoretic fidelity of the injected photon pairs?

Injecting photon pairs as before, the probability-theoretic fidelity f = ∑ k √ pk · p′k between experimentally measured coincidence probabilities at the output of the device (p00, p01, p10, p11) and the ideal theoretical values (p′00, p ′ 01, p ′ 10, p ′ 11) was calculated for each ϕ̃j . 

Q18. What is the description of the experiment?

The Bell-CHSH experiment provides a well-known test for the presence of entanglement that the authors use here to examine the performance of the device, as it is reconfigured across a large parameter space. 

Q19. How many configurations produced photon statistics with f > 0.97?

The average fidelity across 995 configurations (equivalent to many truth tables in many bases) was measured to be 0.990±0.009 with 96% of configurations ϕ̃j producing photon statistics with f > 0.97. 

Q20. What is the fidelity of the entanglement approach?

The authors chose to use the entanglement approach as a more demanding test of their device, demonstrating sufficient control to obtain the data shown in Fig.