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arXiv:quant-ph/0007077

On the quantum mechanical nature in liquid NMR quantum computing

Gui‐Lu Long, Haoxiong Yan, Y s Li, Chang-Cun Tu, Shiyao Zhu, D Ruan, Sun, Y, Tao, J X, H M Chen

Published Jul 20, 2000• 0 citations
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Abstract

The quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed. It is pointed out that the key problem in the current debate is the understanding of entanglement in a mixed state system. The following points are concluded in this Letter: 1)Density matrix describes the "state" of an average particle in an ensemble. It can not describe the state of an individual particle in an ensemble in detail; 2) Entanglement is a property of the wave function of a quantum particle(such as an molecule in a liquid NMR sample). Separability of the density matrix can not be used to measure the entanglement of mixed ensemble; 3)The evolution of states in bulk-ensemble NMR quantum computation is quantum mechanical; 4) The coefficient before the effective pure state density matrix, $ε$, is an measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system. We conclude that the liquid NMR quantum computation is genuine, not just classical simulations.

DOI
10.48550/arxiv.quant-ph/0007077

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The quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed. It is pointed out that the key problem in the current debate is the understanding of entanglement in a mixed state system. The following points are concluded in this Letter: 1)Density matrix describes the "state" of an average particle in an ensemble. It can not describe the state of an individual particle in an ensemble in detail; 2) Entanglement is a property of the wave function of a quantum particle(such as an molecule in a liquid NMR sample). Separability of the density matrix can not be used to measure the entanglement of mixed ensemble; 3)The evolution of states in bulk-ensemble NMR quantum computation is quantum mechanical; 4) The coefficient before the effective pure state density matrix, εεε, is an measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system. We conclude that the liquid NMR quantum computation is genuine, not just classical simulations.
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the state of anaverage particle in an ensemble. It does not describe the of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
The quantum nature of bulk ensemble NMR quantum computing — the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMR quantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of an average particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglement is a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separability of the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMR quantum computation is quantum-mechanical; iv) The coefficient before the effective pure state density matrix, є, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classical simulations.
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an individual molecule coincides with whole sample molecules distribution over single molecule energy levels. This means that quantum stochasticity is replaced by classical stochasticity. In the present paper it is shown, that quantum NMR computation can create genuine entangled states if initial system states are thermodynamical equilibrium ones. A separability analysis problem can arise when one interprets the readout signal from whole sample.
We show that differently constructed ensembles having the same density matrix may be physically distinguished by observing fluctuations of some observables. An explicit expression for fluctuations of an observable in an ensemble is given. This result challenges Peres's fundamental postulate and seems to be contrary to the widely-spread belief that ensembles with the same density matrix are physically identical. This leads us to suggest that the current liquid NMR quantum computing is truly quantum-mechanical in nature.
We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.