Comparison of incoherent operations and measures of coherence

Chitambar, Eric; Gour, Gilad

doi:10.1103/physreva.94.052336

Cited by 232 publications

(289 citation statements)

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“…This letter has adopted the incoherent operations (IO) of Baumgratz et al [3], where each Kraus operator in a measurement just needs to be incoherence-preserving. While the class IO has drawbacks in terms of formulating a full physically consistent resource theory of coherence [11,20], it nevertheless seems unlikely that the results of this letter would remain true if other operational classes were considered. For example, the strictly incoherent operations (SIO) proposed by Yadin et al are unable to convert one eCoBit into a CoBit [11].…”

Section: Theoremmentioning

confidence: 99%

“…(20). In other words, p(x) describes the distribution of outcomes when measuring ∆(Ψ A ) in the incoherent basis.…”

Section: Code Structurementioning

confidence: 99%

“…Systems in such superposition states are often said to possess quantum coherence. There has currently been much interest in constructing a resource theory of quantum coherence [1][2][3][4][5][6][7][8][9][10][11], in part because of recent experimental and numerical findings that suggest quantum coherence alone can enhance or impact physical dynamics in biology [12][13][14][15], transport theory [2,16,17], and thermodynamics [18,19].In a standard resource-theoretic treatment of quantum coherence, the free (or "incoherent") states are those that are diagonal in some fixed reference (or "incoherent") basis Different classes of allowed (or "incoherent") operations have been proposed in the literature [1,3,[9][10][11] (see also [20,21] for comparative studies of these approaches), however an essential requirement is that the incoherent operations act invariantly on the set of diagonal density matrices. Incoherent operations can then be seen as one of the most basic generalizations of classical operations (i.e.…”

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confidence: 99%

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Relating the Resource Theories of Entanglement and Quantum Coherence

2016

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Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations without classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the wellknown Horodecki criterion for distillability.The ability for quantum systems to exist in "superposition states" reveals the wave-like nature of matter and represents a strong departure from classical physics. Systems in such superposition states are often said to possess quantum coherence. There has currently been much interest in constructing a resource theory of quantum coherence [1][2][3][4][5][6][7][8][9][10][11], in part because of recent experimental and numerical findings that suggest quantum coherence alone can enhance or impact physical dynamics in biology [12][13][14][15], transport theory [2,16,17], and thermodynamics [18,19].In a standard resource-theoretic treatment of quantum coherence, the free (or "incoherent") states are those that are diagonal in some fixed reference (or "incoherent") basis Different classes of allowed (or "incoherent") operations have been proposed in the literature [1,3,[9][10][11] (see also [20,21] for comparative studies of these approaches), however an essential requirement is that the incoherent operations act invariantly on the set of diagonal density matrices. Incoherent operations can then be seen as one of the most basic generalizations of classical operations (i.e. stochastic maps) since their action on diagonal states can always be simulated by classical processing. Note also that most experimental setups will have a natural basis to work in, and arbitrary unitary time evolutions might be physically difficult to implement. In these settings, there are practical advantages to identifying "diagonal preserving" operations as being "free" relative to coherentgenerating ones.One does not need to look far to find an important connection between incoherent operations and quantum entanglement, the latter being one of the most important resources in quantum information processing [22]. Consider the task of entanglement generation. This procedure is usually modeled by bringing together two or more quantum syst...

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Section: Theoremmentioning

confidence: 99%

“…(20). In other words, p(x) describes the distribution of outcomes when measuring ∆(Ψ A ) in the incoherent basis.…”

Section: Code Structurementioning

confidence: 99%

mentioning

confidence: 99%

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Relating the Resource Theories of Entanglement and Quantum Coherence

2016

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“…In addition, various other coherence measures were discussed [10][11][12][13][14][15][16][17]. Many further discussions about quantum coherence were aroused [18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Ordering states with Tsallis relative $$\alpha $$ α -entropies of coherence

Zhang

Shao

Luo

et al. 2016

Quantum Inf Process

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In this paper, we study the ordering states with Tsallis relative α-entropies of coherence and l1 norm of coherence for single-qubit states. We show that any Tsallis relative α-entropies of coherence and l1 norm of coherence give the same ordering for single-qubit pure states. However, they don't generate the same ordering for some high dimensional pure states, even though these states are pure. We also consider three special Tsallis relative α-entropies of coherence, such as C1 ,C2 and C 1 2 , and show any one of these three measures and C l 1 will not generate the same ordering for single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states.

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“…However, as is the case with entanglement, there exists no unique quantifier of coherence. Problems of physical consistency arising out of basis dependent formulations of coherence measures have been noted [27]. On the other hand, basis independent measures of coherence have also been formulated [28], [29], which manifest intrinsic randomness contained in a quantum state.…”

Section: Introductionmentioning

confidence: 99%

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

Chatterjee

Majumdar

2017

Phys. Rev. A

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We consider the effect of relativistic boosts on single particle Gaussian wave packets. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence it is shown that in general the coherence decays with the increase of the momentum of the state, as well as the boost applied to it. Employing a basis-independent formulation, we show however, that coherence may be preserved even for large boosts applied on narrow uncertainty wave packets. Our result is exemplified quantitatively for practically realizable neutron wave functions.

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Comparison of incoherent operations and measures of coherence

Cited by 232 publications

References 39 publications

Relating the Resource Theories of Entanglement and Quantum Coherence

Relating the Resource Theories of Entanglement and Quantum Coherence

Ordering states with Tsallis relative $$\alpha $$ α -entropies of coherence

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

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