arXiv:hep-th/0501058 · Journal of Statistical Mechanics Theory and Experiment

Entanglement induced fluctuations of cold bosons

Ram Brustein, Amos Yarom

Published Jul 29, 2008• 3 citations

Abstract

We show that due to entanglement, quantum fluctuations may differ significantly from statistical fluctuations. We calculate quantum fluctuations of the particle number and of the energy in a sub-volume of a system of bosons in a pure state, and briefly discuss the possibility of measuring them. We find that energy fluctuations have a non-extensive nature.

DOI: 10.1088/1742-5468/2008/07/p07025

Related papers

Entanglement Induced Fluctuations of Cold Bosons

Brustein, R, Yarom, A

We show that due to entanglement, quantum fluctuations may differ significantly from standard statistical fluctuations. We calculate quantum fluctuations of the particle number and of the energy in a sub-volume of a system of bosons in a pure state, and briefly discuss the possibility of measuring them. We explain how area-scaling of the energy fluctuations may be relevant to black hole physics.

Jan 9, 20053 citations

Boson-fermion universality of mesoscopic entanglement fluctuations in free systems

Cunzhong Lou, Chushun Tian, Zhixing Zou +2 more

Entanglement fluctuations associated with the Schrödinger evolution of wave functions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of the present authors showed that, in a class of free-fermion lattice models and interacting spin chains, entanglement dynamics enters into a new regime at long time, with entanglement probes displaying persistent temporal fluctuations, whose statistics falls into the seemingly disparate paradigm of mesoscopic fluctuations in condensed-matter physics. This motivates us to revisit here entanglement dynamics of a canonical bosonic model in many-body physics, i.e., a coupled harmonic oscillator chain. We find that when the system is driven out of equilibrium, the long-time entanglement dynamics exhibits strictly the same statistical behaviors as those of free-fermion models. Specifically, irrespective of entanglement probes and microscopic parameters, the statistical distribution of entanglement fluctuations is flanked by asymmetric tails: sub-Gaussian for upward fluctuations and sub-Gamma for downward; moreover, the variance exhibits a crossover from the scaling ∼ 1 / L to ∼ L A 3 / L 2 as the subsystem size L A increases ( L the total system size). This insensitivity to the particle statistics, dubbed boson-fermion universality, is contrary to the common wisdom that statistical phenomena of a many-body nature depend strongly on particle statistics. Together with our previous work, the present study indicates rich fluctuation phenomena in long-time entanglement dynamics that await in-depth exploration.

arXiv:2411.14687Physical Review ResearchMay 30, 20251 citation

Quantum entanglement

Franck Laloë

In this chapter, we study the properties of quantum entanglement, and more generally the way correlations can appear in quantum mechanics. Quantum entanglement is an important notion that we have already discussed, for instance in the context of the Von Neumann chain or of the Schrödinger cat, but here we give more details on its properties. In classical physics, the notion of correlation is well known. It hinges on the calculation of probabilities and on linear averages over a number of possibilities. A distribution gives the probability of having the first system in a some given state and the second in another state. If this distribution is not a product, the two systems are correlated. If it is a product, they are uncorrelated; measuring the properties of one system does not bring any information on the other. This is in particular the case if the state of each of the two systems is perfectly defined (which also defines the state of the whole system perfectly well). The notion of correlation between sub-systems therefore stems from the multiplicity of possible states of the whole system; fluctuations of this state are necessary to give its full meaning to the classical notion of correlation. In quantum mechanics, the situation is different: as we have seen (in particular in Chapter 4), even a physical system that is perfectly defined by a given state vector already contains fluctuations.

Cambridge University Press eBooksAug 30, 20121 citation

Entanglement of bosonic systems under monitored evolution

Quancheng Liu, K. Ziegler

The evolution of noninteracting bosons in the presence of repeated projective measurements is studied. Following the established approach, this monitored evolution is characterized by the first detected return and the first detected transition probabilities. We show that these quantities are directly related to the entanglement entropy and the entanglement spectrum of a bipartite system. Calculations with specific values for the number of bosons, the number of measurements, and the time steps between measurements reveal a sensitive and often strongly fluctuating entanglement entropy. In particular, we demonstrate that in the vicinity of special values for the time steps, the evolution of the entanglement entropy either is stationary or performs dynamical switching between two or more stationary values. In the entanglement spectrum, on the other hand, this complex behavior can be associated with level crossings, indicating that the dominant quantum states and their entanglement respond strongly to a change of the system parameters. We discuss briefly the role of time averaging to remove the fluctuations of the entanglement entropy.

arXiv:2403.06297Physical Review AAug 5, 20242 citations

Entanglement Transfer from Bosonic Systems to Qubits

Andrzej Veitia

We study the entanglement of a pair of qubits resulting from their interaction with a bosonic system. Here we restrict our discussion to the case where the set of operators acting on different qubits commute. A special class of interactions inducing entanglement in an initially separable two qubit system is discussed. Our results apply to the case where the initial state of the bosonic system is represented by a statistical mixture of states with fixed particle number.

arXiv:0902.2234Feb 13, 20091 citation

Quantum Entanglement for Systems of Identical Bosons. I General Theory

Bryan J. Dalton, John Goold, B. M. Garraway +1 more

These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. We focus on the meaning of entanglement, the quantum paradoxes associated with entangled states, and important tests that allow an experimentalist to determine whether a quantum state - in particular, one for massive bosons is entangled. Our tests for entanglement fully utilise the symmetrisation principle and super-selection rules for bosonic massive particles. These papers provides detailed arguments necessary for the conclusions of a recent paper which presented results for rigorously demonstrating the entanglement of a two-mode Bose-Einstein condensate (BEC). In the first paper (I), we discuss the meaning of entanglement for systems of identical particles. For such systems, the relevant quantum density operators must satisfy the symmetrisation principle and global and local super-selection rules prohibiting states in which there are coherences between differing particle numbers. We fully justify these requirements. In the second quantisation approach, both the system and sub-systems are modes (or sets of modes) rather than particles, particles being associated with different mode occupancies. In the accompanying review paper (II), we consider spin squeezing and other tests for entanglement for two-mode bosonic systems. Starting from paper (I) we determine which tests are useful for detecting entanglement in massive bosonic (BEC), as opposed to photonic, systems. Several new inequalities are derived, and recent key experiments are analysed.

arXiv:1506.06906Jun 23, 20151 citation