<p>Coherence and magic (non-stabilizerness), as two different types of quantum resources playing fundamental roles in quantum information, have been widely studied separately. In this work, we reveal some intrinsic connections between them by characterizing and quantifying magic as the minimal coherence relative to the MUBs generated by the pure stabilizer states. This is motivated by the observation that in the stabilizer formalism of quantum computation, all pure stabilizer states in a prime-dimensional quantum system can be partitioned into <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$d+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> MUBs, and a pure state contains no magic if and only if it is incoherent relative to at least one of these <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$d+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> MUBs. We introduce quantifiers of magic via the minimal coherence relative to the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$d+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> MUBs and compare them with some popular ones. Using the quantifiers of magic generated by the relative entropy of coherence and the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$l_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm of coherence, we evaluate the magic of some important states in low dimensional systems. Furthermore, we show the optimality of the quantum <i>T</i>-gates for generating magic resource in terms of our quantifiers of magic, which is consistent with previous results based on other quantifiers of magic.</p>

Magic as Minimal Coherence Relative to Mutually Unbiased Bases

期刊论文
发表日期：

2026年1月14日

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Zijian Zhang,
Shunlong Luo,
Yue Zhang

摘要

Coherence and magic (non-stabilizerness), as two different types of quantum resources playing fundamental roles in quantum information, have been widely studied separately. In this work, we reveal some intrinsic connections between them by characterizing and quantifying magic as the minimal coherence relative to the MUBs generated by the pure stabilizer states. This is motivated by the observation that in the stabilizer formalism of quantum computation, all pure stabilizer states in a prime-dimensional quantum system can be partitioned into $d+1$ $d + 1$ MUBs, and a pure state contains no magic if and only if it is incoherent relative to at least one of these $d+1$ $d + 1$ MUBs. We introduce quantifiers of magic via the minimal coherence relative to the $d+1$ $d + 1$ MUBs and compare them with some popular ones. Using the quantifiers of magic generated by the relative entropy of coherence and the $l_1$ $l_{1}$ -norm of coherence, we evaluate the magic of some important states in low dimensional systems. Furthermore, we show the optimality of the quantum T-gates for generating magic resource in terms of our quantifiers of magic, which is consistent with previous results based on other quantifiers of magic.