期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 68, 期 7, 页码 4518-4530出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2022.3157440
关键词
Encoding; Entropy; Decoding; Testing; Quantum system; Extraterrestrial measurements; Thermodynamics; Encoding; quantum mechanics; quantum entanglement
资金
- Foundation for Polish Science through International Research Agenda Project (IRAP) by European Union (EU) within Smart Growth Operational Program [2018/MAB/5]
- TEAM-NET Project [POIR.04.04.00-00-17C1/18-00]
- National Science Center in Poland [DEC-2015/18/A/ST2/00274]
- Polish National Science Centre [2016/22/E/ST6/00062]
- National University of Singapore (NUS) [R-263-000-E32-133, R-263-000-E32-731]
- National Research Foundation, Prime Minister's Office, Singapore
- Ministry of Education, Singapore, through the Research Centres of Excellence Program
We analyze the problem of encoding classical information into different resources of a quantum state, considering a general class of communication scenarios. For any state, we find upper bounds on the number of messages that can be encoded using the operations, as well as matching lower bounds in the case of a specific resource destroying map. In the asymptotic setting, our bounds provide an operational interpretation of resource monotones.
We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is the twirling channel over some unitary group, we find matching one-shot lower bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.
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