The q-fermion numbers emerging from the q-fermion oscillator algebra are used to reproduce the q-fermionic Stirling and Bell numbers. New recurrence relations for the expansion coefficients in the 'anti-normal ordering' of the q-fermion operators are derived. The roles of the q-fermion numbers in q-stochastic point processes and the Bargmann space representation for q-fermion operators are explored.
In this article we present an analysis to derive physical results in the entanglement amplification of fermonic systems in the relativistic regime, that is, beyond the single-mode approximation. This leads a recent work in [M. Montero and E. Martín-Martínez, JEHP 07 (2011) 006] to a physical result, and solidifies that phenomenon of entanglement amplification can actually happen in the relativistic regime.
Physically Motivated Ansatz for Open Fermionic Systems on Quantum Computer
State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China（中国科学技术大学精密与智能化学国家重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each conta…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even and odd parity fermionic states. It thereby characterizes the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective m…
The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance of the GPCs is confirmed by analytical means for the ground state in the regime of weak couplings by finding its vector of natural occupation numbers close to the boundary of the allowed region. Such quasipinning is found to become weaker in the intermediate and strong coupling regime. The study of crossovers between different spatial dimensions by detuning t…
Quantum simulations of fermionic many-body systems crucially rely on mappings from indistinguishable fermions to distinguishable qubits. The non-local structure of fermionic Fock space necessitates encodings that either map local fermionic operators to non-local qubit operators, or encode the fermionic representation in a long-range entangled code space. In this latter case, there is an unavoidable trade-off between two desirable properties of the encoding: low weight representations of local fermionic operators, and a high distance code space. Here it is argued that despite this fundamental l…
Engineering non-Markovianity from spectral shaping of bosonic and fermionic baths
Fudan University（复旦大学）；University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory（合肥国家实验室）；University of California San Diego（加利福尼亚大学圣迭戈分校）
Sandia National Laboratories（桑迪亚国家实验室）；DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心 DAMTP）；Department of Physics and Astronomy, Dartmouth College（达特茅斯学院物理与天文学系）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算科学联合中心）；School of Physics, University of Sydney（悉尼大学物理学院）；Department of Chemistry, Rice University（莱斯大学化学系）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）
This paper deals with the mathematical spectral analysis and physical interpretation of a fermionic system described by a non-Hermitian Hamiltonian possessing real eigenvalues. A statistical thermodynamical description of such a system is considered. Approximate expressions for the energy expectation value and the number operator expectation value, in terms of the absolute temperature $T$ and of the chemical potential $μ$, are obtained, based on the Euler-Maclaurin formula.
In this comment we show that the ambiguity of entropic quantities calculated in Physical Review A 83, 062323 (2011) for fermionic fields in the context of Unruh effect is not related to the properties of anticommuting fields, as claimed in Physical Review A 83, 062323 (2011), but rather to wrong mathematical manipulations with them and not taking into account a fundamental superselection rule of quantum field theory.
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and lowering operators play a relevant role in this analysis. The technical problem of our approach stands in the difficulty of solving the equations of motion, which are, first of all, {\em operator-valued} and, secondly, quite often nonlinear. In this paper we construct a general procedure which significantly simplifies the treatment for those systems which can b…
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call "m-type" and "q-type" particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have n…
The Pauli exclusion principle as constraint on fermionic occupation numbers is a consequence of the much deeper fermionic exchange statistics. Just recently, it was shown by Klyachko that this antisymmetry of fermionic wave functions leads to further restrictions on natural occupation numbers. These so-called generalized Pauli constraints (GPC) significantly strengthen Pauli's exclusion principle. Our first goal is to develop an understanding of the mathematical concepts behind Klyachko's work, in the context of quantum marginal problems. Afterwards, we explore the physical relevance of GPC an…
We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time …
Majorana-fermionic quantum computation (MFQC) was proposed by Bravyi and Kitaev (See Ref.\cite{Kitaev}), in which a fault-torrent (non-topological) quantum computer built from Majorana fermions may be more efficient than that built from distinguishable two-state systems. However, till now people don't know how to realize a MFQC in a physical system. In this paper we proposed a possible realization of MFQC. We find that the end of a line-defect of p-wave superconductor or superfluid on a honeycomb lattice will trap a Majorana zero mode, which will become the starting point of MFQC. Then we show…
