In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $ρ$ can be determined by finding the expectation value of an observable on $m$ copies of $ρ$, without performing state tomography. Since a circuit exists which can approximate the measurement of any observable, in principle one can find a circuit which will estimate any such polynomial function by averaging over many runs. I construct some simple examples and compare these results to existing procedures.
We present networks for directly estimating the polynomial invariants of multi-party quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multi-party states, where each party can have a Hilbert space of …
In this paper, we present a fast quantum algorithm to measure the Hamming distance between two or more Boolean functions provided as black-boxes. The proposed algorithm constructs a new black-box with a certain property which is utilized to solve this problem. The introduced algorithm converts measuring the Hamming distance between Boolean functions to measuring entanglement between qubits, using concurrence entanglement measure.
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering experiments require massive, slow, projectiles with kinetic energies lower than the first excitation of the system in question. The results of such experiments can have a (probabilistic) distribution (as is the case when the Born approximation for the scattering is valid) or be deterministic (in a semi-classical limit).
We study the possibility of reconstructing the quantum state of light in a cavity subject to dissipation. We pass atoms, also subject to decay, through the cavity and surprisingly show that both decays allow the measurement of $s$-parametrized quasiprobability distributions. In fact, if we consider only atomic decay, we show that the Wigner function may be reconstructed. Because these distributions contain whole information of the initial field state, it is possible to recover information after both atomic and field decays occur.
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented which can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field causing simple harmonic oscillation in the transverse dir…
In this thesis we present a direct scheme for measuring quasidistribution functions of light. This scheme, based on photon counting, is derived from a simple relation linking the Wigner function with photon statistics. We develop a full multimode theory of the scheme, and show that the principle of the measurement can be straightforwardly generalized to the detection of the multimode radiation. We also discuss practical aspects of the scheme, including statistical error, non-unit detection efficiency, and imperfect interference visibility. Next, we report experimental realization of the scheme…
We propose a new method to directly measure a general multi-particle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wavefunction of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measu…
Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.
Temporal-spectral modes of light provide a fundamental window into the nature of atomic and molecular systems and offer robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the single-photon level thus play a central role in understanding quantum emitters and are a key requirement for quantum technologies that harness single-photon states. Here we demonstrate an optical reference-free method, which melds techniques from ultrafast metrology and single-photon spectral detection, to characterize the temporal-spectral state of single phot…
We analyze the possibility of measuring the state of a movable mirror by using its interaction with a quantum field. We show that measuring the field quadratures allows to reconstruct the characteristic function corresponding to the mirror state.
A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states.
We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to fully a connected many-particle system such as a bosonic Josephson junction or spins with long-range interactions. In these systems the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an $N$ body system can also be accurately extracted from the long-time OTOC dynamics, however, for short…
Efficiently and Reliably Measuring Information Processing Capacity in Dynamical Systems via Kernels
School of Computer Science and Statistics, Trinity College Dublin（都柏林三一学院计算机科学与统计学院）；Trinity Quantum Alliance（三一量子联盟）；School of Physics（物理学院）；Trinity College Dublin（都柏林三一学院）
We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is explicitly given. We administered written free-response and multiple-choice questions to investigate these difficulties. We find that students have common difficulties with these concepts. We discuss some of the findings.
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. Here we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. The protocol accounts for both pure and mixed initial states, and is applicable to systems that interact with environmen…
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems generally. Measuring them requires an echo-type sequence in which the sign of a many-body Hamiltonian is reversed. We detail an implementation employing cold atoms and cavity quantum electrodynamics to realize the chaotic kicked top model, and we analyze effects of dissipation to verify its feasibility with current technology. Finally, we propose in broad str…
We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid opto-/electro-mechanical devices, where the theoretical proposals discussed in our work could find an experim…
Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex partition function zeroes of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates, local spin rotations, and projective measurements along two orthogonal quantization axes. Besides presentin…
We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, an…
Recent work proposed a variant on Ramsey interferometry for coupled spin-$1/2$ systems that directly measures the retarded spin-spin Green's function. We expand on that work by investigating nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excit…
Measuring correlations using local and nonlocal quenches
Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别杰夫物理研究所）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；National Research University Higher School of Economics（国立高等经济大学）
There is an enormous amount of information that can be extracted from the data of a quantum gas microscope that has yet to be fully explored. The quantum gas microscope has been used to directly measure magnetic order, dynamic correlations, Pauli blocking, and many other physical phenomena in several recent groundbreaking experiments. However, the analysis of the data from a quantum gas microscope can be pushed much further, and when used in conjunction with theoretical constructs it is possible to measure virtually any observable of interest in a wide range of systems. We focus on how to meas…
