arXiv subjects

Emanuel Knill

Publications and source records attributed to Emanuel Knill.

At least 37 records · Page 2Linked to original sources

arXiv2021

High-fidelity indirect readout of trapped-ion hyperfine qubits

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a $^9\text{Be}^+$ qubit ion is mapped to a $^{25}\text{Mg}^+$ readout ion using laser-driven Raman transitions. By partitioning the $^9\text{Be}^+$ ground state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of $1.2^{+1.1}_{-0.6} \times 10^{-4}$ and $0^{+1.9}_{-0} \times 10^{-5}$ with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.

quant-ph↗

arXiv2021

Device-independent Randomness Expansion with Entangled Photons

With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is consumed. Here, we devise a device-independent spot-checking protocol that consumes only uniform bits without requiring any additional bits with a specific bias. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640). The experiment ran for 91.0 hours, creating randomness at an average rate of 3606 bits/s with a soundness error bounded by $5.7\times 10^{-7}$ in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and may one day enable high-quality private sources of randomness as the device footprint shrinks.

quant-ph↗

arXiv2021

Direct observation of deterministic macroscopic entanglement

Quantum entanglement of mechanical systems emerges when distinct objects move with such a high degree of correlation that they can no longer be described separately. Although quantum mechanics presumably applies to objects of all sizes, directly observing entanglement becomes challenging as masses increase, requiring measurement and control with a vanishingly small error. Here, using pulsed electromechanics, we deterministically entangle two mechanical drumheads with masses of 70 pg. Through nearly quantum-limited measurements of the position and momentum quadratures of both drums, we perform quantum state tomography and thereby directly observe entanglement. Such entangled macroscopic systems are uniquely poised to serve in fundamental tests of quantum mechanics, enable sensing beyond the standard quantum limit, and function as long-lived nodes of future quantum networks.

quant-ph↗

arXiv2021

Scalable multiphoton quantum metrology with neither pre- nor post-selected measurements

The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric down-conversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling and quantum networks.

quant-ph↗

arXiv2019

Experimental Low-Latency Device-Independent Quantum Randomness

Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of $512$ bits with an average experiment time of less than $5$ min per block and with a certified error bounded by $2^{-64}\approx 5.42\times 10^{-20}$.

quant-ph↗

arXiv2019

Quantum gate teleportation between separated qubits in a trapped-ion processor

Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling with individually-addressed single-qubit rotations and detections, same- and mixedspecies two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.

quant-ph↗

arXiv2019

Certified Quantum Measurement of Majorana Fermions

We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\langle W \rangle \le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\langle W \rangle=5$ indicates the degree of confidence in the detection of Majorana fermions.

quant-ph↗

arXiv2019

Approximate exchange-only entangling gates for the three-spin-$1/2$ decoherence-free subsystem

The three-spin-$1/2$ decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combinations of logical Pauli products not involving $σ_y$ can be implemented directly. Self-inverse gates that are constructible from these Hamiltonians, such as the CNOT, can be implemented without the assumption on the physical spins. We compare the control complexity of implementing CNOT to previous methods and find that the complexity for fault-tolerant fidelities is competitive.

quant-ph↗

arXiv2018

Certifying Quantum Randomness by Probability Estimation

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation can take advantage of verifiable physical constraints, and the certification is with respect to classical side information. Examples include randomness from single-photon measurements and device-independent randomness from Bell tests. Advantages of probability estimation include adaptability to changing experimental conditions, unproblematic early stopping when goals are achieved, optimal randomness rates, applicability to Bell tests with small violations, and unsurpassed finite-data efficiency. We greatly reduce latencies for producing random bits and formulate an associated rate-tradeoff problem of independent interest. We also show that the latency is determined by an information-theoretic measure of nonlocality rather than the Bell violation.

quant-ph↗

arXiv2018

Quantum Randomness Generation by Probability Estimation with Classical Side Information

We develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can stop performing trials early, as soon as the desired amount of randomness is extractable. It can be used with arbitrary, partially known and time-dependent probabilities for the random settings choices. Furthermore, it is suitable for application to experimental configurations with low Bell violation per trial, such as current optical loophole-free Bell tests. It is possible to adapt to time-varying experimental parameters. We formulate the framework for the general situation where the trial probability distributions are constrained to a known set. Randomness expansion with logarithmic settings entropy is possible for many relevant configurations. We implement probability estimation numerically and apply it to a representative settings-conditional probability distribution of the outcomes from an atomic loophole-free Bell test [Rosenfeld et al., Phys. Rev. Lett. 119:010402 (2017), arXiv:1611.04604 (2016)] to illustrate trade-offs between the amount of randomness, error, settings entropy, unknown settings biases, and number of trials. We then show that probability estimation yields more randomness from the loophole-free Bell-test data analyzed in [Bierhorst et al., arXiv:1702.05178 (2017)] and tolerates adversarial settings probability biases.

quant-ph↗

arXiv2018

Quantum Process Fidelity Bounds from Sets of Input States

We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. The minimal non-orthogonal symmetric POVM contains $d+1$ states, where $d$ is the Hilbert space dimension. Our bounds applied to these states provide an efficient method for estimating the process fidelity without the use of full process tomography.

quant-ph↗

arXiv2018

Measurement-based entanglement of noninteracting bosonic atoms

We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom interactions. In contrast, in our work we use Hong-Ou-Mandel interference to postselect a spin-singlet state after overlapping two atoms in distinct spin states on an effective beam splitter. We verify the presence of entanglement and determine a bound on the postselected fidelity of a spin-singlet state of $\left(0.62 \pm 0.03\right)$. The experiment has direct analogy to creating polarization entanglement with single photons and hence demonstrates the potential to use protocols developed for photons to create complex quantum states with noninteracting atoms.

physics.atom-ph↗

arXiv2018

Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within $10^{-12}$. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

quant-ph↗

arXiv2017

Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials

Given a composite null hypothesis H, test supermartingales are non-negative supermartingales with respect to H with initial value 1. Large values of test supermartingales provide evidence against H. As a result, test supermartingales are an effective tool for rejecting H, particularly when the p-values obtained are very small and serve as certificates against the null hypothesis. Examples include the rejection of local realism as an explanation of Bell test experiments in the foundations of physics and the certification of entanglement in quantum information science. Test supermartingales have the advantage of being adaptable during an experiment and allowing for arbitrary stopping rules. By inversion of acceptance regions, they can also be used to determine confidence sets. We use an example to compare the performance of test supermartingales for computing p-values and confidence intervals to Chernoff-Hoeffding bounds and the "exact" p-value. The example is the problem of inferring the probability of success in a sequence of Bernoulli trials. There is a cost in using a technique that has no restriction on stopping rules, and for a particular test supermartingale, our study quantifies this cost.

math.ST↗

arXiv2017

Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

quant-ph↗

arXiv2016

A strong loophole-free test of local realism

We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p-values as small as $5.9\times 10^{-9}$ for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p-value is $2.3 \times 10^{-7}$. We therefore reject the hypothesis that local realism governs our experiment.

quant-ph↗

arXiv2014

Bell Inequalities for Continuously Emitting Sources

A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have "jitter", coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-realistic system to show apparent violation--the so-called "coincidence loophole". Here we introduce a family of Bell inequalities based on signed, directed distances between the parties' sequences of recorded timetags. Given that the timetags are recorded for synchronized, fixed observation periods and that the settings choices are random and independent of the source, violation of these inequalities unambiguously shows non-classical correlations violating local realism. Distance-based Bell inequalities are generally useful for two-party configurations where the effective size of the measurement outcome space is large or infinite. We show how to systematically modify the underlying Bell functions to improve the signal to noise ratio and to quantify the significance of the violation.

quant-ph↗

arXiv2014

Tunable spin-spin interactions and entanglement of ions in separate wells

Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our setup we select one that entangles the internal states of the two ions with 0.82(1) fidelity. Extension of this building-block to a 2D-network, which ion-trap micro-fabrication processes enable, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of intriguing condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient.

quant-ph↗