181 research outputs found
Deconstruction and conditional erasure of quantum correlations
We define the deconstruction cost of a tripartite quantum state on systems ABE as the minimum rate of noise needed to apply to the
AE systems, such that there is negligible disturbance to the marginal state on the BE systems, while the system A of the resulting state is locally recoverable from the
E system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems ABE is equal to its conditional quantum mutual information (CQMI) I(A;B|E), thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems
AE in order to decouple system A from systems BE, while causing negligible disturbance to the marginal state of systems BE. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI I(A;B|E). State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction and/or conditional erasure if Alice has available the best possible system
E to help in the deconstruction and/or conditional erasure task
Conditional decoupling of quantum information
Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Phys. Rev. A 72, 032317 (2005)PLRAAN1050-294710.1103/PhysRevA.72.032317] showed that the quantum mutual information I(A;B) quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems AB. Here, we investigate correlations in tripartite systems ABE. In particular, we are interested in the minimal rate of noise needed to apply to the systems AE in order to erase the correlations between A and B given the information in system E, in such a way that there is only negligible disturbance on the marginal BE. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states ABE. Our main result is that both are equal to the conditional quantum mutual information I(A;B|E) - establishing it as an operational measure for tripartite quantum correlations
Conditional quantum one-time pad
Suppose that Alice and Bob are located in distant laboratories, which are
connected by an ideal quantum channel. Suppose further that they share many
copies of a quantum state , such that Alice possesses the
systems and Bob the systems. In our model, there is an identifiable part
of Bob's laboratory that is insecure: a third party named Eve has infiltrated
Bob's laboratory and gained control of the systems. Alice, knowing this,
would like use their shared state and the ideal quantum channel to communicate
a message in such a way that Bob, who has access to the whole of his laboratory
( systems), can decode it, while Eve, who has access only to a sector of
Bob's laboratory ( systems) and the ideal quantum channel connecting Alice
to Bob, cannot learn anything about Alice's transmitted message. We call this
task the conditional one-time pad, and in this paper, we prove that the optimal
rate of secret communication for this task is equal to the conditional quantum
mutual information of their shared state. We thus give the
conditional quantum mutual information an operational meaning that is different
from those given in prior works, via state redistribution, conditional erasure,
or state deconstruction. We also generalize the model and method in several
ways, one of which demonstrates that the negative tripartite interaction
information of a tripartite state
is an achievable rate for a secret-sharing task, i.e., the case in
which Alice's message should be secure from someone possessing only the or
systems but should be decodable by someone possessing all systems ,
, and .Comment: v2: 16 pages, final version accepted for publication in Physical
Review Letter
Disentanglement cost of quantum states.
We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman et al., Phys. Rev. A 72, 032317 (2005)PLRAAN1050-294710.1103/PhysRevA.72.032317] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically transform the state to a locally recoverable version of the state
Entanglement-assisted private communication over quantum broadcast channels
We consider entanglement-assisted (EA) private communication over a quantum
broadcast channel, in which there is a single sender and multiple receivers. We
divide the receivers into two sets: the decoding set and the malicious set. The
decoding set and the malicious set can either be disjoint or can have a finite
intersection. For simplicity, we say that a single party Bob has access to the
decoding set and another party Eve has access to the malicious set, and both
Eve and Bob have access to the pre-shared entanglement with Alice. The goal of
the task is for Alice to communicate classical information reliably to Bob and
securely against Eve, and Bob can take advantage of pre-shared entanglement
with Alice. In this framework, we establish a lower bound on the one-shot EA
private capacity. When there exists a quantum channel mapping the state of the
decoding set to the state of the malicious set, such a broadcast channel is
said to be degraded. We establish an upper bound on the one-shot EA private
capacity in terms of smoothed min- and max-entropies for such channels. In the
limit of a large number of independent channel uses, we prove that the EA
private capacity of a degraded quantum broadcast channel is given by a
single-letter formula. Finally, we consider two specific examples of degraded
broadcast channels and find their capacities. In the first example, we consider
the scenario in which one part of Bob's laboratory is compromised by Eve. We
show that the capacity for this protocol is given by the conditional quantum
mutual information of a quantum broadcast channel, and so we thus provide an
operational interpretation to the dynamic counterpart of the conditional
quantum mutual information. In the second example, Eve and Bob have access to
mutually exclusive sets of outputs of a broadcast channel.Comment: v2: 23 pages, 2 figures, accepted for publication in the special
issue "Shannon's Information Theory 70 years on: applications in classical
and quantum physics" for Journal of Physics
Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
Quantum error correction (QEC) is a procedure by which the quantum state of a
system is protected against a known type of noise, by preemptively adding
redundancy to that state. Such a procedure is commonly used in quantum
computing when thermal noise is present. Interestingly, thermal noise has also
been known to play a central role in quantum thermodynamics (QTD). This fact
hints at the applicability of certain QTD statements in the QEC of thermal
noise, which has been discussed previously in the context of Maxwell's demon.
In this article, we view QEC as a quantum heat engine with a feedback
controller (i.e., a demon). We derive an upper bound on the measurement heat
dissipated during the error-identification stage in terms of the Groenewold
information gain, thereby providing the latter with a physical meaning also
when it is negative. Further, we derive the second law of thermodynamics in the
context of this QEC engine, operating with general quantum measurements.
Finally, we show that, under a set of physically motivated assumptions, this
leads to a fundamental triple trade-off relation, which implies a trade-off
between the maximum achievable fidelity of QEC and the super-Carnot efficiency
that heat engines with feedback controllers have been known to possess. A
similar trade-off relation occurs for the thermodynamic efficiency of the QEC
engine and the efficacy of the quantum measurement used for error
identification
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