The symmetric extendibility of quantum states

Nowakowski, Marcin

doi:10.1088/1751-8113/49/38/385301

Cited by 6 publications

(10 citation statements)

References 34 publications

(85 reference statements)

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“…On the other hand due to results in Ref. [46] and the fact that K → D (ρ ps ) = log 2 dim H (ρ ps ) both one-way and two-way keys are lower bounded…”

Section: And the Lower Bound Formentioning

confidence: 97%

Hybrid quantum network design against unauthorized secret-key generation, and its memory cost

Sakarya

Winczewski

Rutkowski

et al. 2020

Phys. Rev. Research

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A significant number of servers that constitute the Internet are to provide private data via private communication channels to mutually anonymous registered users. Such are the servers of banks, hospitals that provide cloud storage and many others. Replacing communication channels by maximally entangled states is a promising idea for the quantum-secured Internet (QI). While it is an important idea for large distances secure communication, for the case of the mentioned class of servers pure entanglement based solution is not only unnecessary but also opens a threat. A crack stimulating a node to generate secure connections via entanglement swapping between two hackers can cause uncontrolled consumption of resources. Turning into positive a recently proven no-go result by S. Bäuml et al. [Nat. Commun. 6, 6908 (2015)], we propose a natural countermeasure against this threat. The solution bases on connections between hub-nodes and end-users realized with states that contain secure key but do not allow for swapping of this key. We then focus on the study of the quantum memory cost of such a scheme and prove a fundamental lower bound on its memory overhead. In particular, we show that to avoid the possibility of entanglement swapping, it is necessary to store at least twice as much memory than it is the case in standard quantum-repeater-based network design. For schemes employing either states with positive partial transposition that approximates certain privates states or private states hardly distinguishable from their attacked versions, we derive much tighter lower bounds on required memory. Our considerations yield upper bounds on a two-way repeater rate for states with positive partial transposition (PPT), which approximates strictly irreducible private states. As a byproduct, we provide a lower bound on the trace distance between PPT and private states, shown previously only for private bits.

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“…On the other hand due to results in Ref. [46] and the fact that K → D (ρ ps ) = log 2 dim H (ρ ps ) both one-way and two-way keys are lower bounded…”

Section: And the Lower Bound Formentioning

confidence: 97%

Hybrid quantum network design against unauthorized secret-key generation, and its memory cost

Sakarya

Winczewski

Rutkowski

et al. 2020

Phys. Rev. Research

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show abstract

“…This observation follows directly from the Fuchs-van de Graaf inequality [40], which for two arbitrary states ρ, σ reads 1 2 || 1 ρ − σ|| ≤ 1 − F (ρ, σ), and the fact that (not regularised) one-way distillable key is asymptotically continuous (see Lemma V.3 in [37]). We use fidelity which is calculated for a map Γ A→A a maximising the fidelity of recovery in (69).…”

Section: A Lower Bound On the Loss Of The Distillable Key For Private...mentioning

confidence: 87%

“…To conclude about the non-lockability of the raw key obtained in the one-way protocol we invoke first the main result of Devetak and Winter in [9]. Theorem 3 ([9], in formulation of [37]). For every state ρ ABE , K → = lim n→∞ K (1) (ρ ⊗n ) n…”

Section: Lower Bound For the Drop Of Generated Key Under Erasure Of A...mentioning

confidence: 99%

“…This allows us for estimating closeness of single copy oneway secure key K (1) → between state ρ AaBE and its recovered version ρ A aBE . In what follows, we use lemma V.3 of [37] for the case of triparite states (for biparite states it needs correction, see Lemma 3 presented in the Appendix).…”

Section: A Lower Bound On the Loss Of The Distillable Key For Private...mentioning

confidence: 99%

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Upper bounds on the leakage of private data and operational approach to markovianity

Horodecki,

Studziński,

Kostecki

et al. 2021

Preprint

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We quantify consequences of a leakage of the private key and private randomness generated during quantum key distribution. We provide simple lower bounds on the one-way distillable key after the leakage has been detected. We also show that the distributed private randomness does not drop down by more than twice the number of qubits of the traced-out system. We further focus on strictly irreducible private states, showing that their two-way distillable key is to same extent non-lockable. We achieve this by referring to the idea of recovery maps. We then consider special case of side-channels on some of private states. With the view of usage of the latter states in the hybrid quantum network we consider private state construction based on quantum secrete sharing and show its limitations. Finally, in analogy to a recent result of J. Ko lodyński et al. [Phys. Rev. A 101, 020303(R) (2020)], we connect the topic of (non)markovian dynamics with that of hacking. In particular, we show that an invertible map is non-CP-divisible if and only if there exists a state whose the key witness by a particular privacy witness increases in time.

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“…The maximally entangled state of a bipartite system shared between Alice and Bob in space is represented as |Ψ AB = 1 √ d i |ii . For the sake of spatial quantum entanglement, it is crucial to define the reductions of multipartite states and their extensions [12]. To find a reduced state ρ A of a local state possessed e.g.…”

Section: Quantum Entanglement In Timementioning

confidence: 99%

Quantum entanglement in time

Nowakowski

2017

AIP Conference Proceedings

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In this paper we present a concept of quantum entanglement in time in a context of entangled consistent histories. These considerations are supported by presentation of necessary tools closely related to those acting on a space of spatial multipartite quantum states. We show that in similarity to monogamy of quantum entanglement in space, quantum entanglement in time is also endowed with this property for a particular history. Basing on these observations, we discuss further bounding of temporal correlations and derive analytically the Tsirelson bound implied by entangled histories for the Leggett-Garg inequalities.

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The symmetric extendibility of quantum states

Cited by 6 publications

References 34 publications

Hybrid quantum network design against unauthorized secret-key generation, and its memory cost

Hybrid quantum network design against unauthorized secret-key generation, and its memory cost

Upper bounds on the leakage of private data and operational approach to markovianity

Quantum entanglement in time

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