arXiv subjects

Ezad Shojaee

Publications and source records attributed to Ezad Shojaee.

8 recordsLinked to original sources

arXiv2026

Quantified convergence of general homodyne measurements with applications to continuous variable quantum computing

In arXiv:2503.00188 we introduced broadband pulsed (BBP) homodyne measurements as a generalization of standard pulsed homodyne quadrature measurements. BBP can take advantage of detectors such as calorimeters that have the potential for high efficiency over a broad spectral range. BBP homodyne retains the advantages of standard pulsed homodyne, enabling measurement of arbitrary quadratures in the limit of large amplitude local oscillators (LO). Here we quantify the convergence of standard and BBP homodyne quadrature measurements to those of the quadrature of interest. We obtain lower bounds on the fidelity of the post-measurement classical-quantum state of outcomes and unmeasured modes, and the fidelity of the states obtained after applying operations conditional on measurement outcomes. The bounds depend on the LO amplitude and the moments of number operators. We demonstrate the practical relevance of these bounds by evaluating them for standard pulsed homodyne used for estimating values of the characteristic function of the Wigner distribution, expectations of moments, for quantum teleportation and for continuous variable error correction with GKP codes.

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arXiv2025

Broadband pulsed quadrature measurements with calorimeters

A general one-dimensional quantum optical mode is described by a shape in the time or frequency domain. A fundamental problem is to measure a quadrature operator of such a mode. If the shape is narrow in frequency this can be done by pulsed homodyne detection, in which the mode and a matched local oscillator (LO) interfere on a beamsplitter, whose output ports are monitored by photo-detectors. The quadrature value is proportional to the difference between the photo-detectors' signals. When the shape of the mode is broad in frequency, the lack of uniform response of the detectors across the spectrum prevents direct application of this technique. We show that pulsed homodyne detection can be generalized to broadband pulsed (BBP) homodyne detection setups with detectors such as calorimeters that detect total energy instead of total number of photons. This generalization has applications in quantum measurements of femtosecond pulses, and, speculatively, measurements of Rindler modes to verify the temperature of Unruh radiation. Like pulsed homodyne detection, BBP homodyne detection requires choosing the LO pulse such that the subtracted signal approaches the desired quadrature measurement for large LO amplitudes. A distinctive feature of the technique is that the LO pulse does not belong to the mode of the quadrature being measured. We analyze how the implemented measurement approaches an ideal quadrature measurement with growing LO amplitude. We prove that the moments of the measurement converge to the moments of the quadrature and that the measurement distributions converge weakly.

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arXiv2023

Filter functions for the Glauber-Sudarshan $P$-function regularization

The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter functions that are introduced to regularize the Glauber-Sudarshan $P$ function. We show that the quantum map associated with a filter function is completely positive and trace preserving and hence physically realizable if and only if the Fourier transform of this function is a probability density distribution. We also derive a lower bound on the fidelity between the input and output states of a physical quantum filtering map. Therefore, based on these results, we show that any quantum state can be approximated, to arbitrary accuracy, by a quantum state with a regular Glauber-Sudarshan $P$ function. We propose applications of our results for estimating the output state of an unknown quantum process and estimating the outcome probabilities of quantum measurements.

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arXiv2022

Constraints on Gaussian Error Channels and Measurements for Quantum Communication

Joint Gaussian measurements of two quantum systems can be used for quantum communication between remote parties, as in teleportation or entanglement swapping protocols. Many types of physical error sources throughout a protocol can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study joint Gaussian measurements on two modes $\mathsf{A}$ and $\mathsf{B}$ that take place after independent single-mode Gaussian error channels, for example loss with parameters $l_\mathsf{A}$ and $l_\mathsf{B}$ followed by added noise with parameters $n_\mathsf{A}$ and $n_\mathsf{B}$. We show that, for any Gaussian measurement, if $l_\mathsf{A} + l_\mathsf{B} + n_\mathsf{A} + n_\mathsf{B} \geq 1$ then the effective total measurement is separable and unsuitable for teleportation or entanglement swapping of arbitrary input states. If this inequality is not satisfied then there exists a Gaussian measurement that remains inseparable. We extend the results and determine the set of pairs of single-mode Gaussian error channels that render all Gaussian measurements separable.

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arXiv2021

Entanglement Thresholds of Doubly-Parametric Quantum Transducers

Doubly-parametric quantum transducers, such as electro-opto-mechanical devices, are quickly approaching quantum operation as decoherence mechanisms such as thermal noise, loss, and limited cooperativities are improved. These devices show potential as the critical link between quantum information contained at frequencies as disparate as those in the optical and microwave domains, thus enabling applications such as long distance networking of superconducting quantum computers. However, the requirements on the operating parameters of the transducers necessary to achieve quantum operation have yet to be characterized. In this work we find simple, explicit expressions for the necessary and sufficient conditions under which doubly-parametric transducers in the resolved-sideband, steady-state limit are capable of entangling optical and microwave modes. Our analysis treats the transducer as a two-mode bosonic Gaussian channel capable of both beamsplitter-type and two-mode squeezing-type interactions between optical and microwave modes. For the beamsplitter-type interaction, we find parameter thresholds which distinguish regions of the channel's separability, capacity for bound entanglement, and capacity for distillable entanglement. By contrast, the two-mode squeezing-type interaction always produces distillable entanglement with no restrictions on temperature, cooperativities, or losses. Finally, we find the entanglement breaking conditions on the reduced one-mode upconversion and downconversion channels obtained by initializing the unused input with vacuum while ignoring the unused output. These differences between the entanglement thresholds of the beamsplitter-type and two-mode squeezing-type interactions are then important considerations in the construction of larger quantum networks that integrate multiple transducers.

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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.

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arXiv2020

Squeezing the angular momentum of an ensemble of complex multi-level atoms

Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field, or by state dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so atoms behave like pseudo-spin-$1/2$ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of $\sim 10^6$ Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of $\gtrsim -5$dB was generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise has allowed us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Thus, our work sets the stage for experiments on quantum feedback, deterministic squeezing, closed-loop magnetometry, and new types of quantum simulation based on continuous QND measurement and feedback.

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arXiv2018

Optimal Pure-State Qubit Tomography via Sequential Weak Measurements

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

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