Catalytic quantum teleportation and beyond

Lipka-Bartosik, Patryk; Skrzypczyk, Paul

doi:10.48550/arxiv.2102.11846

Cited by 4 publications

(5 citation statements)

References 56 publications

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“…where δ 2 pδq OE 0 as δ OE 0, and the first inequality follows from (19) and the second follows from the result of Lemma 2. Using the above inequality, and applying expectation to (18), we obtain…”

Section: E Analysis Of Trace Distancementioning

confidence: 99%

Multi-Party Quantum Purity Distillation with Bounded Classical Communication

Atif¹,

Pradhan²

2022

Preprint

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We consider the task of distilling local purity from a noisy quantum state ρ ABC , wherein we provide a protocol for three parties, Alice, Bob and Charlie, to distill local purity (at a rate P ) from many independent copies of a given quantum state ρ ABC . The three parties have access to their respective subsystems of ρ ABC , and are provided with pure ancilla catalytically, i.e., with the promise of returning them unaltered after the end of the protocol. In addition, Alice and Bob can communicate with Charlie using a one-way multiple-access dephasing channel of link rates R 1 and R 2 , respectively. The objective of the protocol is to minimize the usage of the dephasing channel (in terms of rates R 1 and R 2 ) while maximizing the asymptotic purity that can be jointly distilled from ρ ABC . To achieve this, we employ ideas from distributed measurement compression protocols, and in turn, characterize a set of sufficient conditions on pP, R 1 , R 2 q in terms of quantum information theoretic quantities such that P amount of purity can be distilled using rates R 1 and R 2 . Finally, we also incorporate the technique of asymptotic algebraic structured coding, and provide a unified approach of characterizing the performance limits. a measurement apparatus is initialized in a pure state. For this reason, the second law of thermodynamics recognizes purity as indeed a resource [1], [2]. In this regard, the idea of distilling of local purity was first introduced in [3], [4] where the aim was to manipulate the qubits and concentrate the existing diluted form of purity. Two version of this problem have been introduced, (i) a single-party variant and (ii) a distributed version. In the former single-party scenario, also called as local purity concentration, many copies of a noisy state ρ A are provided to Alice, and she aims at concentrating or extracting purity using only unitary operations. The authors in [5] characterized the asymptotic performance limit of this protocol (κpρ A q) as the difference between the number of qubits describing the system and the von Neumann entropy of the state ρ A . For the latter case of distilling purity from a non-local distributed state, commonly termed as local purity distillation, two parties, Alice and Bob, share many copies of the noisy state ρ AB and aim at jointly distilling pure ancilla qubits. Again, they are allowed to perform only local unitaries and but can communicate classically (LOCC), possibly through the use of a dephasing channel [3]. Further, the protocols for both the variants require isolation (Closed-LOCC) from the environment which eliminated the possibility of unlimited consumption of the pure ancilla qubits. The authors in [4] provided bounds for this problem in the one-way and the two-way classical communication scenarios.Later, Devetak in [6] considered a new paradigm called 1-CLOCC 1 , which was defined as an extension of Closed-LOCC, with (i) the allowance of using additional catalytic pure ancilla as long as these are returned back to the system, and (ii) the ...

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Section: E Analysis Of Trace Distancementioning

confidence: 99%

Multi-Party Quantum Purity Distillation with Bounded Classical Communication

Atif¹,

Pradhan²

2022

Preprint

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“…The concept of catalysis was also used in enhancing success probability in some quantum information processing tasks like entanglement concentration [18,19]. Recently it was shown that catalyst can improve quantum teleportation protocol [20]. By sharing a catalyst state between two parties during quantum teleportation results in a higher fidelity rate.…”

Section: Introductionmentioning

confidence: 99%

Catalytic Transformations in Coherence Theory

Char¹,

Chakraborty²,

Bhar³

et al. 2021

Preprint

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In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic setup. Though relative entropy of coherence introduced in 2014 by T. Baumgratz ( Physical Review Letters 113 (14) (2014) 140401) as a coherence measure but it's operational meaning in single copy setup was unknown so far. Here we have provided relative entropy of coherence (via IO (Incoherent Operations)) and coherence of formation (via IO) and quantum incoherent relative entropy (via LQICC(Local Quantum Incoherent Operations with Classical Communications)) a clear operational significance in single copy setup using the concept of catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, LICC(Local Incoherent Operations with Classical Communications) and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging, in single copy setup using catalyst. Monotone property of relative entropy of coherence, coherence of formation and quantum incoherent relative entropy under the catalytic transformation are also discussed here.

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“…The particular appeal of the set CCO(ρ) is that for some prominent resource theories it is fully characterised by a single resource monotone, e.g., the entanglement entropy [22] or the non-equilibrium free energy [37]. It is also of operational interest since it contains states that are strictly more useful than ρ for some information-theoretic tasks, for example quantum teleportation [23]. Figure 1 gives an example of these sets and their full characterisation for the resource theory of athermality restricted to states that commute with the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Fundamental Limits on Correlated Catalytic State Transformations

Roberto¹,

Tomamichel²

2021

Preprint

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Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a catalyst system that assists the transformation and is returned unchanged, but potentially correlated, with the target state. While this has been an active area of recent research, very little is known about the necessary properties of such catalysts. Here, we prove fundamental limits applicable to any correlated catalytic transformation by showing that a small residual correlation between catalyst and target state implies that the catalyst needs to be highly resourceful. In fact, the resources required diverge in the limit of vanishing residual correlation. We develop our results in a general resource theory framework and discuss its implications for the resource theory of athermality, the resource theory of coherence and entanglement theory.

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Catalytic quantum teleportation and beyond

Cited by 4 publications

References 56 publications

Multi-Party Quantum Purity Distillation with Bounded Classical Communication

Multi-Party Quantum Purity Distillation with Bounded Classical Communication

Catalytic Transformations in Coherence Theory

Fundamental Limits on Correlated Catalytic State Transformations

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