Photon-number moments and cumulants of Gaussian states
- URL: http://arxiv.org/abs/2212.06067v4
- Date: Fri, 17 Nov 2023 17:55:58 GMT
- Title: Photon-number moments and cumulants of Gaussian states
- Authors: Yanic Cardin, Nicol\'as Quesada
- Abstract summary: We develop expressions for the moments and cumulants of Gaussian states when measured in the photon-number basis.
We show that the calculation of photon-number moments and cumulants are $#P$-hard.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We develop closed-form expressions for the moments and cumulants of Gaussian
states when measured in the photon-number basis. We express the photon-number
moments of a Gaussian state in terms of the loop Hafnian, a function that when
applied to a $(0,1)$-matrix representing the adjacency of a graph, counts the
number of its perfect matchings. Similarly, we express the photon-number
cumulants in terms of the Montrealer, a newly introduced matrix function that
when applied to a $(0,1)$-matrix counts the number of Hamiltonian cycles of
that graph. Based on these graph-theoretic connections, we show that the
calculation of photon-number moments and cumulants are $#P$-hard. Moreover, we
provide an exponential time algorithm to calculate Montrealers (and thus
cumulants), matching well-known results for Hafnians. We then demonstrate that
when a uniformly lossy interferometer is fed in every input with identical
single-mode Gaussian states with zero displacement, all the odd-order cumulants
but the first one are zero. Finally, we employ the expressions we derive to
study the distribution of cumulants up to the fourth order for different input
states in a Gaussian boson sampling setup where $K$ identical states are fed
into an $\ell$-mode interferometer. We analyze the dependence of the cumulants
as a function of the type of input state, squeezed, lossy squeezed, squashed,
or thermal, and as a function of the number of non-vacuum inputs. We find that
thermal states perform much worse than other classical states, such as squashed
states, at mimicking the photon-number cumulants of lossy or lossless squeezed
states.
Related papers
- Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom.
These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
arXiv Detail & Related papers (2024-06-26T18:27:15Z) - Multi-mode Gaussian State Analysis with one Bounded Photon Counter [0.0]
What properties of a multi-mode Gaussian state are determined by the signal from one detector that measures total number photons up to some bound?
We find that if the Gaussian state occupies $S$ modes and the probabilities of $n$ photons for all $nleq 8S$ are known, then we can determine the spectrum of the Gaussian covariance matrix.
Nothing more can be learned, even if all photon-number probabilities are known.
arXiv Detail & Related papers (2024-04-13T10:44:33Z) - Average Rényi Entanglement Entropy in Gaussian Boson Sampling [17.695669245980124]
We study the modal entanglement of the output states in a framework for quantum computing.
We derive formulas for $alpha = 1$, and, more generally, for all integers $alpha$ in the limit of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength.
arXiv Detail & Related papers (2024-03-27T18:00:01Z) - Quantum tomography of helicity states for general scattering processes [65.268245109828]
Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics.
We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
arXiv Detail & Related papers (2023-10-16T21:23:42Z) - Theory of free fermions under random projective measurements [43.04146484262759]
We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers.
We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
arXiv Detail & Related papers (2023-04-06T15:19:33Z) - Average entanglement entropy of midspectrum eigenstates of
quantum-chaotic interacting Hamiltonians [0.0]
We show that the magnitude of the negative $O(1)$ correction is only slightly greater than the one predicted for random pure states.
We derive a simple expression that describes the numerically observed $nu$ dependence of the $O(1)$ deviation from the prediction for random pure states.
arXiv Detail & Related papers (2023-03-23T18:00:02Z) - Gaussian Quantum Illumination via Monotone Metrics [6.626330159001871]
We show that two-mode squeezed vacuum (TMSV) states are the optimal probe among pure Gaussian states with fixed signal mean photon number.
Third, we show that it is of utmost importance to prepare an efficient idler memory to beat coherent states and provide analytic bounds on the idler memory transmittivity in terms of signal power, background noise, and idler memory noise.
arXiv Detail & Related papers (2023-02-15T07:13:04Z) - Average-case Speedup for Product Formulas [69.68937033275746]
Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems.
We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states.
Our results open doors to the study of quantum algorithms in the average case.
arXiv Detail & Related papers (2021-11-09T18:49:48Z) - A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations [31.761854762513337]
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms.
Motivated by existing deterministic and random methods, we present a hybrid approach.
arXiv Detail & Related papers (2021-09-16T13:53:12Z) - Quantum impurity models using superpositions of fermionic Gaussian
states: Practical methods and applications [0.0]
We present a practical approach for performing a variational calculation based on non-orthogonal fermionic Gaussian states.
Our method is based on approximate imaginary-time equations of motion that decouple the dynamics of each state forming the ansatz.
We also study the screening cloud of the two-channel Kondo model, a problem difficult to tackle using existing numerical tools.
arXiv Detail & Related papers (2021-05-03T18:00:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.