Universality of Schmidt decomposition and particle identity
arXiv:1609.03239 · doi:10.1038/srep44675
Abstract
Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to exist for identical particles, an open problem forbidding its application to analyze such many-body quantum systems. Here we prove, using a newly developed approach, that the Schmidt decomposition exists for identical particles and is thus universal. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information theory when particle identity counts as a resource.
arXiv comment8 pages, 4 figures
References in corpus (40)
- Quantum entanglement
- Many-Body Physics with Ultracold Gases
- Quantum-enhanced measurements: beating the standard quantum limit
- Atom chip based generation of entanglement for quantum metrology
- Unified View of Quantum and Classical Correlations
- Quantum Entanglement in Fermionic Lattices
- Controlled exchange interaction between pairs of neutral atoms in an optical lattice
- Quantum Correlations in Systems of Indistinguishable Particles
- Quantum Correlations in Two-Fermion Systems
- The entanglement of indistinguishable particles shared between two parties
- Digital quantum simulation of fermionic models with a superconducting circuit
- Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation
- General criterion for the entanglement of two indistinguishable particles
- Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits
- Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
- Noise suppression using symmetric exchange gates in spin qubits
- Quantum Correlations in Two-Boson Wavefunctions
- Essential entanglement for atomic and molecular physics
- Manipulating biphotonic qutrits
- Stimulated Raman adiabatic passage in a three-level superconducting circuit
- Entanglement in a two-identical-particle system
- Extracting entanglement from identical particles
- Entangling two transportable neutral atoms via local spin exchange
- Cooper Pair Splitting by means of Graphene Quantum Dots
- Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
- Entanglement and Particle Identity: A Unifying Approach
- Quantum entanglement of identical particles by standard information-theoretic notions
- Linear entropy as an entanglement measure in two-fermion systems
- Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon
- Spatial entanglement of bosons in optical lattices
- Fermionic statistics suppresses Fano resonances
- Bipartite entanglement in systems of identical particles: the partial transposition criterion
- Entanglement of Indistinguishable Particles
- Entanglement robustness and geometry in systems of identical particles
- Quantum teleportation with identical particles
- Entanglement in helium
- Unfrustrated Qudit Chains and their Ground States
- Entanglement Witnesses for Indistinguishable Particles
- Dissipative quantum metrology in manybody systems of identical particles
- Performances and robustness of quantum teleportation with identical particles
Cited by in corpus (24)
- Indistinguishability of elementary systems as resource for quantum information processing
- Entanglement in indistinguishable particle systems
- Dealing with indistinguishable particles and their entanglement
- Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks
- Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation
- identical particles and one particle to entangle them all
- Entanglement of indistinguishable particles: a comparative study
- Activating remote entanglement in a quantum network by local counting of identical particles
- Remarks on entanglement and identical particles
- Entanglement of Identical Particles and Coherence in the First Quantization Language
- Entanglement robustness via spatial deformation of identical particle wave functions
- Experimental quantum phase discrimination enhanced by controllable indistinguishability-based coherence
- An algorithm to explore entanglement in small systems
- Indistinguishability-enhanced entanglement recovery by spatially localized operations and classical communication
- Definitions of entwinement
- Mechanistic Understanding of Entanglement and Heralding in Cascade Emitters
- Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy
- Generation of genuine multipartite entangled states via indistinguishability of identical particles
- Role of indistinguishability and entanglement in Hong-Ou-Mandel interference and finite bandwidth effects of frequency entangled photons
- Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators
- Entanglement of condensed magnons via momentum-space fragmentation
- Taming identical particles for discerning the genuine non-locality
- Strategies for generating separable photon triplets in waveguides and ring resonators
- Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits