Macroscopic superpositions require tremendous measurement devices

We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such as generated in previous experiments this is not a stringent restriction, for macroscopic superpositions of the size of a cat the required effort quickly becomes intractable, requiring measurement devices of the size of the Earth. We illustrate our results using macroscopic superposition states of photons, spins, and position. Finally, we also show how this limitation can be circumvented by dealing with superpositions in relative degrees of freedom.

[1]  N. D. Mermin,et al.  Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s , 1980 .

[2]  H. Araki,et al.  Measurement of Quantum Mechanical Operators , 1960 .

[3]  M. Ozawa.  Conservation laws, uncertainty relations, and quantum limits of measurements. , 2001, Physical review letters.

[4]  E. Bagan,et al.  Quantum reverse engineering and reference-frame alignment without nonlocal correlations , 2004 .

[5]  N. Gisin,et al.  Demonstration of Light-Matter Micro-Macro Quantum Correlations. , 2016, Physical review letters.

[6]  Pavel Sekatski,et al.  Macroscopic quantum states: Measures, fragility, and implementations , 2017, Reviews of Modern Physics.

[7]  T. Rudolph,et al.  Reference frames, superselection rules, and quantum information , 2006, quant-ph/0610030.

[8]  A. Falcon.  Physics I.1 , 2018 .

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

[10]  Joonwoo Bae,et al.  Quantum state discrimination and its applications , 2015, 1707.02571.

[11]  G Chiribella,et al.  Efficient use of quantum resources for the transmission of a reference frame. , 2004, Physical review letters.

[12]  N. Gisin,et al.  Size of quantum superpositions as measured with classical detectors , 2013, 1306.0843.

[13]  G. D’Ariano,et al.  Optimal estimation of group transformations using entanglement , 2005, quant-ph/0506267.

[14]  Emmy Noether,et al.  Invariant Variation Problems , 2005, physics/0503066.

[15]  Seung-Woo Lee,et al.  Generation of hybrid entanglement of light , 2014, Nature Photonics.

[16]  Meinhard E. Mayer,et al.  Group theory and physics , 1994 .

[17]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .

[18]  L. Susskind,et al.  Charge Superselection Rule , 1967 .

[19]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[20]  W. Zurek.  Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[21]  B. Julsgaard,et al.  Experimental long-lived entanglement of two macroscopic objects , 2001, Nature.

[22]  Wiseman,et al.  Optimal states and almost optimal adaptive measurements for quantum interferometry , 2000, Physical review letters.

[23]  Pavel Sekatski,et al.  How difficult is it to prove the quantumness of macroscropic states? , 2014, Physical review letters.

[24]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[25]  J. Cirac,et al.  Optimal Purification of Single Qubits , 1998, quant-ph/9812075.

[26]  Are there fundamental limits for observing quantum phenomena from within quantum theory , 2010, 1009.2654.

[27]  A. I. Lvovsky,et al.  Observation of micro–macro entanglement of light , 2013 .

[28]  S. Haroche.  Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary , 2013 .

[29]  E. Wigner.  Die Messung quantenmechanischer Operatoren , 1952 .

[30]  S. Gerlich,et al.  A Kapitza–Dirac–Talbot–Lau interferometer for highly polarizable molecules , 2007, 0802.3287.

[31]  Caslav Brukner,et al.  Classical world arising out of quantum physics under the restriction of coarse-grained measurements. , 2007, Physical review letters.

[32]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[33]  Eugene P. Wigner,et al.  The Intrinsic Parity of Elementary Particles , 1952 .

[34]  Philippe Grangier,et al.  Generation of optical ‘Schrödinger cats’ from photon number states , 2007, Nature.

[35]  K. Audenaert,et al.  Discriminating States: the quantum Chernoff bound. , 2006, Physical review letters.

[36]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[37]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[38]  L. Viola,et al.  Generalized coherent states as preferred states of open quantum systems , 2006, quant-ph/0609068.

[39]  S. Girvin,et al.  Deterministically Encoding Quantum Information Using 100-Photon Schrödinger Cat States , 2013, Science.

[40]  Anton Zeilinger,et al.  Wave–particle duality of C60 molecules , 1999, Nature.

[41]  Giulio Chiribella,et al.  Covariant quantum measurements that maximize the likelihood , 2004, quant-ph/0403083.

[42]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[43]  Marcel Mayor,et al.  Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000 amu. , 2013, Physical chemistry chemical physics : PCCP.

[44]  A. Holevo.  Statistical decision theory for quantum systems , 1973 .

[45]  Chiara Vitelli,et al.  Entanglement test on a microscopic-macroscopic system. , 2008, Physical review letters.

[46]  Habib,et al.  Coherent states via decoherence. , 1993, Physical review letters.