ENTANGLED IDENTICAL PARTICLES AND NOISE

For systems of identical Bosons, it is necessary to reformulate the notions of separability and entanglement in algebraic terms shifting the emphasis from the particle aspect of first quantization to the mode description typical of second quantization. Within this new framework, we show that, unlike for systems consisting of distinguishable qubits, negativity is an exhaustive bipartite entanglement witness for systems with fixed number of Bosons; further, we investigate the impact of dephasing noise in relation to the use of such many-body Bosonic systems in metrological applications.

[1]  C. Caves.  Quantum Mechanical Noise in an Interferometer , 1981 .

[2]  Lorenza Viola,et al.  A subsystem-independent generalization of entanglement. , 2004, Physical review letters.

[3]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[4]  Michael M. Wolf,et al.  Entanglement in fermionic systems , 2007, 0705.1103.

[5]  M. Lewenstein,et al.  Quantum Correlations in Systems of Indistinguishable Particles , 2002, quant-ph/0203060.

[6]  Gerard J. Milburn,et al.  Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential , 1997 .

[7]  Entanglement of two-mode Bose-Einstein condensates , 2002, quant-ph/0209122.

[8]  Mark Fannes,et al.  Quantum Dynamical Systems , 2001 .

[9]  Augusto Smerzi,et al.  Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed-vacuum light. , 2007, Physical review letters.

[10]  Yun Li,et al.  Spin squeezing in a bimodal condensate: spatial dynamics and particle losses , 2008, 0807.1580.

[11]  P. Zoller,et al.  Many-particle entanglement with Bose–Einstein condensates , 2000, Nature.

[12]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[13]  Holland,et al.  Interferometric detection of optical phase shifts at the Heisenberg limit. , 1993, Physical review letters.

[14]  Hans J. Briegel,et al.  Spin squeezing and entanglement , 2008, 0806.1048.

[15]  J I Cirac,et al.  Spin squeezing inequalities and entanglement of N qubit states. , 2005, Physical review letters.

[16]  Fabio Benatti,et al.  Dynamics, Information and Complexity in Quantum Systems , 2009, Theoretical and Mathematical Physics.

[17]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[18]  Bing He,et al.  Creation of high-quality long-distance entanglement with flexible resources , 2008, 0808.2320.

[19]  Many-particle entanglement in two-component Bose-Einstein condensates , 2002, cond-mat/0205369.

[20]  Wineland,et al.  Squeezed atomic states and projection noise in spectroscopy. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[21]  Cirac,et al.  Inseparability criterion for continuous variable systems , 1999, Physical review letters.

[22]  Barry C. Sanders,et al.  Spin squeezing and pairwise entanglement for symmetric multiqubit states , 2003 .

[23]  P. Meystre,et al.  Quantum states for Heisenberg-limited interferometry , 2007 .

[24]  J. Ignacio Cirac,et al.  Quantum entanglement theory in the presence of superselection rules (15 pages) , 2004 .

[25]  D. Spehner,et al.  Effect of phase noise on useful quantum correlations in Bose Josephson junctions , 2011, 1105.4495.

[26]  Luca Marinatto,et al.  Entanglement and Properties of Composite Quantum Systems: A Conceptual and Mathematical Analysis , 2001 .

[27]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[28]  D. Spehner,et al.  Noise in Bose Josephson junctions: Decoherence and phase relaxation , 2009, 0911.0655.

[29]  U. Marzolino,et al.  Sub-shot-noise quantum metrology with entangled identical particles , 2010, 1001.3313.

[30]  Philippe Bouyer,et al.  Heisenberg-limited spectroscopy with degenerate Bose-Einstein gases , 1997 .

[31]  Yun Li,et al.  Optimum spin squeezing in Bose-Einstein condensates with particle losses. , 2008, Physical review letters.

[32]  Fabio Benatti,et al.  Entanglement and squeezing with identical particles: ultracold atom quantum metrology , 2011 .

[33]  Milburn,et al.  Optimal quantum measurements for phase estimation. , 1995, Physical review letters.

[34]  A. Sinatra,et al.  Phase dynamics of Bose-Einstein condensates: Losses versus revivals , 1998, physics/9802040.

[35]  Yun Li,et al.  Atom-chip-based generation of entanglement for quantum metrology , 2010, Nature.

[36]  K. Rzążewski,et al.  Background atoms and decoherence in optical lattices , 2009, 0909.2515.

[37]  D. Petz.  Quantum Information Theory and Quantum Statistics , 2007 .

[38]  P. Zanardi.  Quantum entanglement in fermionic lattices , 2002 .

[39]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[40]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[41]  Ueda,et al.  Squeezed spin states. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[42]  M. Oberthaler,et al.  Nonlinear atom interferometer surpasses classical precision limit , 2010, Nature.

[43]  H M Wiseman,et al.  Entanglement of indistinguishable particles shared between two parties. , 2003, Physical review letters.

[44]  Yurke.  Input states for enhancement of fermion interferometer sensitivity. , 1986, Physical review letters.

[45]  Lorenza Viola,et al.  A Generalization of Entanglement to Convex Operational Theories: Entanglement Relative to a Subspace of Observables , 2005 .

[46]  H. Narnhofer.  The role of transposition and CPT operation for entanglement , 2003 .

[47]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[48]  M. Oberthaler,et al.  Squeezing and entanglement in a Bose–Einstein condensate , 2008, Nature.

[49]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[50]  Wineland,et al.  Optimal frequency measurements with maximally correlated states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[51]  J. Dalibard,et al.  Many-Body Physics with Ultracold Gases , 2007, 0704.3011.