Negativity of random pure states

Datta, Animesh

doi:10.1103/physreva.81.052312

Cited by 14 publications

(17 citation statements)

References 33 publications

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“…This model for subsystem entropies has been found to be a useful one in many different contexts. The most common applications found in the literature are for bipartite systems [1,10,13,18,19], where subsystem entropies are typically within 1 nat of maximal mixing, but we have argued herein that it is often more useful to look at tri-partite or even multi-partite decompositions of the universe. (Indeed multi-partite decompositions have attracted and continue to attract considerable attention [3,4,6,12,21,83,84].…”

Section: Discussionmentioning

confidence: 99%

“…Also note that ||X|| = tr{ √ X † X}.) Calculating the negativity can often be relatively difficult, though for pure states it simplifies to [9,10]…”

Section: Introductionmentioning

confidence: 99%

“…This is not trivial, but at least tractable [9][10][11]. Another interesting quantity is the quantum discord, although this does not directly characterize the entanglement itself, but instead measures the extent to which the correlation are quantum as opposed to classical [12].…”

Section: Introductionmentioning

confidence: 99%

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Multipartite analysis of average-subsystem entropies

Alonso-Serrano

Visser

2017

Phys. Rev. A

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Blackbody radiation contains (on average) an entropy of 3.9 ± 2.5 bits per photon. If the emission process is unitary, then this entropy is exactly compensated by "hidden information" in the correlations. We extend this argument to the Hawking radiation from GR black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget. The key technical aspect of our calculation is a variant of the "average subsystem" approach developed by Page, which we extend beyond bipartite pure systems, to a tripartite pure system that considers the influence of the environment.

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Section: Discussionmentioning

confidence: 99%

“…Also note that ||X|| = tr{ √ X † X}.) Calculating the negativity can often be relatively difficult, though for pure states it simplifies to [9,10]…”

Section: Introductionmentioning

confidence: 99%

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Multipartite analysis of average-subsystem entropies

Alonso-Serrano

Visser

2017

Phys. Rev. A

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“…Since this is a natural extension of the achievable region we found for D = 2, we conjecture that it is the entire achievable set of negativities, (N For the boundary states (c = 0) the parameters can be eliminated for the Gröbner basis to get the conjectured implicit bound; however already in the D = 3 case, the polynomial is rather complicated, containing 143 terms. It is worth mentioning that naïvely testing the conjecture numerically is nearly hopeless, since the negativities of random states are highly non-uniform throughout the achievable set [25]. Nevertheless, testing for perturbations of our boundary has led to no counter-examples.…”

Section: Fig 2: Achievable Qubit Negativitymentioning

confidence: 99%

Polynomial Monogamy Relations for Entanglement Negativity

Allen

Meyer

2017

Phys. Rev. Lett.

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The notion of non-classical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations-the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under LOCC, and derive a necessary and sufficient inequality which, for the first time, is a non-linear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.The prototypical quantum correlation, entanglement, accounts for many of the effects seen in quantum theory, and there is a significant effort to enslave it as a resource to be manipulated and exploited by quantum engineers [1]. The most striking property of entanglement is its distributability, or lack there of, exemplified by its compliance with, for example, monogamy laws [2] and area laws [3], laws which constrain the shareability of correlations. The former law states that the closer two parties are to being maximally entangled, the more the pair become separated and hidden from all other parties. The latter law requires that for certain types of many-particle ground states split in twain, the entanglement between the parts scales according to the size of the separation boundary. Both laws set the stage for entanglement to play a central role in physics, and an active research community continues to strengthen this role [4].The secludedness of maximally entangled states has specifically impacted quantum key distribution [5], ground state frustration [6], and even black holes [7]. These perspectives on monogamy have traditionally been understood in terms of multi-qubit networks. In the case of tripartite systems, the monogamy law can be written in terms of concurrence [8], as the following,where C is the concurrence, subscripts label the parties, and the vertical bar denotes the bipartite split across which it is computed. In this way, if C 2 A|BC ≈ C 2 A|B ≈ 1, i.e., A and B are maximally entangled, then C 2 A|C ≈ 0, hence the personification of entanglement.The elegance and simplicity of the monogamy inequality has made it the paragon for entanglement shareability. It has since been shown that other entanglement measures such as entanglement of formation [9], squashed entanglement [10], and entanglement negativity [11], all satisfy the same monogamy relation. This raises two issues: the monogamy inequality may just be a first order approximation to the shareability of correlational resources, so to what extent can we quantify the exact amount possible to share? Second, is the limited shareability a consequence of limited systems, i.e., qubits?The first issue has recent...

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“…It can be computed easily for arbitrary states of a composite system. Therefore, it has received various studies [6][7][8][9][10]. However, quantum entanglement does not account for all of the non-classical properties of quantum phenomenons.…”

Section: Introductionmentioning

confidence: 99%

Quantum Correlations in Qutrit-Qutrit Systems under Local Quantum Noise Channels

2014

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Due to decoherence, realistic quantum systems inevitably interact with the environment when quantum information is processed, which causes the loss of quantum properties. As a fundamental issue of quantum properties, quantum correlations have attracted a lot of interests in recent years. Because of the importance of high dimensional systems in quantum information, in this work, we study the quantum correlations affected by the Markovian environment by considering the quantum correlations of qutrit-qutrit quantum systems measured by the negativity and the geometric discord. The local noise channels covered in this work includes dephasing, tritflip, trit-phase-flip, and depolarising channels. We have also investigated the cases where the local decoherence channels of two sides are identical and non-identical.

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Negativity of random pure states

Cited by 14 publications

References 33 publications

Multipartite analysis of average-subsystem entropies

Multipartite analysis of average-subsystem entropies

Polynomial Monogamy Relations for Entanglement Negativity

Quantum Correlations in Qutrit-Qutrit Systems under Local Quantum Noise Channels

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