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Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit
P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. Thompson, J. L. O'Brien
TL;DR
Entangled states are fundamental to quantum information, while controlled mixture is important for characterizing devices. This paper uses a reconfigurable photonic circuit to prepare and measure entangled and mixed states, reporting high fidelity across configuration tests and target mixed states.
Problem
Entangled states are fundamental resources in quantum information, and controlled mixture is important for device characterization and proposed waveguide simulations of biological processes.
Source: Generating and characterising… · p. 3, Generating and characterising mixture · p. 4Method
A reconfigurable circuit combines state preparation, a postselected CNOT, arbitrary-basis measurement, and photon tracing to prepare single-qubit states with tunable mixture.
Source: A reconfigurable quantum photonic… · p. 1, Generating and characterising mixture · p. 4Results
Across 995 configurations, average fidelity was 0.990 ± 0.009; Bell-manifold fit R^2 was 0.935, and 119 mixed-state targets averaged 0.98 ± 0.02 fidelity.
Source: Benchmarking of reconfigurability · p. 3, A Bell-type inequality manifold · p. 4, Generating and characterising mixture · p. 4Takeaways & Limitations
Tracing over one output photon yields arbitrary single-qubit states, with their mixture set by the entanglement of the prepared two-qubit state.
Source: Generating and characterising mixture · p. 4
Abstract
from arXiv · showhide
Entanglement is the quintessential quantum mechanical phenomenon understood to lie at the heart of future quantum technologies and the subject of fundamental scientific investigations. Mixture, resulting from noise, is often an unwanted result of interaction with an environment, but is also of fundamental interest, and is proposed to play a role in some biological processes. Here we report an integrated waveguide device that can generate and completely characterize pure two-photon states with any amount of entanglement and arbitrary single-photon states with any amount of mixture. The device consists of a reconfigurable integrated quantum photonic circuit with eight voltage controlled phase shifters. We demonstrate that for thousands of randomly chosen configurations the device performs with high fidelity. We generate maximally and non-maximally entangled states, violate a Bell-type inequality with a continuum of partially entangled states, and demonstrate generation of arbitrary one-qubit mixed states.
A reconfigurable quantum photonic circuit
The silica-on-silicon circuit encodes two photonic qubits in dual-rail waveguides and combines reconfigurable single-qubit stages with a postselected CNOT. Its first stage prepares states, while the mirrored final stage enables measurement in arbitrary bases.
A reconfigurable quantum photonic circuit
- Two photonic qubits are encoded in pairs of waveguides, with one photon in each upper waveguide as the logical |0A⟩⊗|0B⟩ input.The device is a silica-on-silicon entangling circuit.Source: A reconfigurable quantum photonic… · p. 1
- Pairs of Hadamard-like gates and phase rotations implement the single-qubit stages, while two Hadamard-like gates and a controlled-sign gate together implement the CNOT.The waveguide circuit uses directional couplers and voltage-controlled thermo-optic phase shifters.Source: Figure 1 · p. 1
- The first circuit stage enables arbitrary state preparation, and the central postselected CNOT is a maximally entangling gate that succeeds with probability 1/9.The final stage mirrors the first and enables projective measurement of each qubit in an arbitrary basis.Source: A reconfigurable quantum photonic… · p. 1
- Two phase shifters per Mach-Zehnder interferometer implement reconfigurable single-qubit operations on the inputs and their inverse operations on the outputs.The device uses two Mach-Zehnder interferometers in each of its reconfigurable initial and final stages.Source: A reconfigurable quantum photonic… · p. 2
Benchmarking of reconfigurability
The circuit was tested across randomly selected phase settings after measurements of its classical and quantum interference. Its measured coincidence probabilities closely matched theoretical predictions across the tested configurations.
Benchmarking of reconfigurability
- 0.978 ± 0.007 was the measured Hong-Ou-Mandel dip visibility, accounting for accidental coincidences.The authors say the high visibility indicates high device quality because circuit imperfections could limit the dip visibility.Source: Benchmarking of reconfigurability · p. 2
- The whole-circuit test randomly sampled 995 possible phase configurations and compared measured output coincidence probabilities with ideal theoretical values.The device was also assessed by measuring interference fringes across its eight phase shifters; average fringe contrast was 0.988 ± 0.008.Source: Benchmarking of reconfigurability · p. 2
- 0.990 ± 0.009 was the average fidelity across 995 configurations, and 96% produced photon statistics with f > 0.97.The histogram shows the distribution across the randomly selected eight-phase settings.Source: Figure 3 · p. 3, Benchmarking of reconfigurability · p. 3
Generating and characterising entanglement
The circuit prepares a continuum of entangled, partially entangled, and separable states from computational-basis product inputs. It generated and characterized the four Bell states using quantum state tomography.
Generating and characterising entanglement
- The circuit prepares a continuum of entangled, partially entangled, and separable states from computational-basis product inputs.Superposition states at the CNOT input ideally produce the four corresponding Bell states.Source: Generating and characterising… · p. 3
- Maximum-likelihood quantum state tomography reconstructed the four Bell-state density operators using 16 measurements per state.The final phase shifters implement the arbitrary single-qubit measurement capability used for tomography.Source: Generating and characterising… · p. 3
- The four on-chip Bell states had quantum-state fidelities of 0.947 ± 0.002, 0.945 ± 0.002, 0.933 ± 0.002, and 0.885 ± 0.002, respectively.The figure presents the real parts of the four states’ density operators.Source: Generating and characterising… · p. 3, Figure 4 · p. 3
A Bell-type inequality manifold
The authors map the Bell-CHSH sum across a continuum of entanglement strengths and Bob’s measurement settings. The measured manifold includes violations of the local hidden-variable bound and is compared with its theoretical counterpart.
A Bell-type inequality manifold
- The CHSH test uses the sum of four two-observer correlations, which local hidden-variable models constrain to −2 ≤ S ≤ 2.The authors use this inequality to examine device performance across the parameter space.Source: A Bell-type inequality manifold · p. 3
- The measured Bell-CHSH sum reached 2.49 ± 0.03 and −2.54 ± 0.03, beyond the respective bounds of 2 and −2.The measured manifold is plotted in Fig. 5b.Source: A Bell-type inequality manifold · p. 3, Figure 5 · p. 4
- Varying α tunes the prepared state between product and maximally entangled states, with partially entangled states in between.Bob’s settings vary with β while Alice’s settings remain fixed.Source: A Bell-type inequality manifold · p. 3
- R² = 0.935 for the measured manifold, compared with 1 in the ideal case.R² compares experimental Bell-CHSH sums with theoretical values.Source: A Bell-type inequality manifold · p. 4
Generating and characterising mixture
The device prepares arbitrary single-qubit mixed states by tracing over one photon of an entangled pair, with the pair’s entanglement setting the mixture. Randomly selected targets were reconstructed with high average fidelity, and programmed states also traced Ψ in the Bloch sphere.
Generating and characterising mixture
- Tracing over one output photon prepares an arbitrary single-qubit state, whose mixture is set by the two-qubit state’s entanglement and can span pure to maximally mixed.Adjusting φ1–4 continuously varies the reduced state’s mixture from 0 to 1.Source: Generating and characterising mixture · p. 4
- Average fidelity across 119 randomly chosen mixed-state targets was 0.98±0.02, with 91% above 0.95; 63 generated states traced Ψ in the Bloch sphere.The figure shows the fidelity distribution and the Ψ inset; each inset point comes from a different partially entangled bipartite state.Source: Generating and characterising mixture · p. 4, Figure 6 · p. 5
- Entanglement-based mixture generation was chosen as a more demanding device test and avoids requiring pseudo- or quantum-random number generators in practical applications.The device could instead generate mixture by applying random voltages to phase shifters on a single qubit.Source: Generating and characterising mixture · p. 4
- Controlled entanglement and mixture support quantum-device characterization and testing quantum physics, while controlled mixture may also serve photonic analogues of biochemical systems involving decoherence.Source: Generating and characterising mixture · p. 5
Methods
The methods describe a silica-on-silicon waveguide chip, photon-pair source, and calibration of its voltage-controlled phase shifters. Classical fringes were used to estimate each heater’s phase response, with no crosstalk observed in these experiments.
Methods
- The chip uses 3.5-µm-wide silica waveguides between 16-µm silica cladding layers and measures 70 mm × 3 mm.The waveguide core is silica doped with germanium and boron oxides; the upper cladding is doped with phosphorous and boron.Source: Methods · p. 5
- Degenerate 808 nm photon pairs were produced by focusing a 404 nm, 60 mW laser onto a 2 mm BiBO crystal for type-I spontaneous parametric downconversion.Source: Methods · p. 5
- Each phase shifter’s nonlinear voltage response was calibrated by sweeping heater voltage from 0 V to 7 V and fitting classical interference fringes.The fitted relationship approximates the phase response for each heater; no crosstalk was observed in these experiments.Source: Methods · p. 5
- Single-photon fringes for each phase shifter were measured using photon pairs, with coincidence counting to largely mitigate single-photon detector dark counts.Each fringe was normalized to its amplitude for clarity.Source: Methods · p. 5
Additional information
The authors report no competing financial interests and provide supplementary-information and correspondence details.
Additional information
- The authors declare no competing financial interests.Source: Additional information · p. 7
- Supplementary information accompanies the paper at www.nature.com/naturephotonics.Source: Additional information · p. 7
- Correspondence and materials requests are directed to J.L. O’B.Reprints and permissions information is available online.Source: Additional information · p. 7