Physical purification of quantum states

Kleinmann, Matthias; Kampermann, Hermann; Meyer, T.; Bruß, Dagmar

doi:10.1103/physreva.73.062309

Cited by 26 publications

(23 citation statements)

References 12 publications

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“…In quantum mechanics, this has been noted by Kleinman et al in Ref. [36]. Along the same lines, it is easy to prove the following general Theorem:…”

Section: Lemma 19mentioning

confidence: 65%

Probabilistic theories with purification

2010

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We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamio lkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

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“…In quantum mechanics, this has been noted by Kleinman et al in Ref. [36]. Along the same lines, it is easy to prove the following general Theorem:…”

Section: Lemma 19mentioning

confidence: 65%

Probabilistic theories with purification

2010

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“…Technically, the time evolution of the density matrix is replaced by the time evolution of a state vector which is first constructed by purifying the density matrix. Purification turns a density matrix into a ket state belonging to a larger Hilbert space in a way, that a trace over the additional (auxiliary) degrees of freedom returns the desired density matrix [50,51,52]. Figure 1: Visualization of the enlarged system for a physical spin chain: Green circles connected by black lines mark the spins of the chain, whereas the green circles on top denote ancilla spins.…”

Section: Thermal Dmrgmentioning

confidence: 99%

Thermal density matrix renormalization group for highly frustrated quantum spin chains: A user perspective

Heveling

Richter

Schnack

2019

Journal of Magnetism and Magnetic Materials

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Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.

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“…But S pur is a pair of pure states, for which the optimal success probability is known due to the result by Jaeger and Shimony [6]. The map from S to S pur , on the other hand, can only be performed physically in very special situations [22,23] and hence the success probability of S pur in general only yields an upper bound. This bound is strongly related to the Uhlmann fidelity tr | √ ρ 1 √ ρ 2 | of ρ 1 ≡ γ 1 / tr(γ 1 ) and ρ 2 ≡ γ 2 / tr(γ 2 ) [24,25].…”

Section: Fidelity Form Measurementmentioning

confidence: 99%

Structural approach to unambiguous discrimination of two mixed quantum states

Kleinmann

Kampermann

Bruß

2010

Journal of Mathematical Physics

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We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 ("solution in 4 dimensions"). The solution is illustrated by some examples. The optimality conditions proved by Eldar et al. [Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy.

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Physical purification of quantum states

Cited by 26 publications

References 12 publications

Probabilistic theories with purification

Probabilistic theories with purification

Thermal density matrix renormalization group for highly frustrated quantum spin chains: A user perspective

Structural approach to unambiguous discrimination of two mixed quantum states

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