Page 18 - BE Book PESD 2021 22

can enhance the potential to extract work, in contrast to any of their definite order of
occurrence. Surprisingly, this enhancement is possible even without assigning any
thermodynamic resource value to the input qubits. Further, we provide the first non-trivial
example of causal enhancement using non-unital pin maps.

In addition to the characterization of geometrical state spaces for the passive states, an
operational approach has been introduced to distinguish them on their charging capabilities of
a quantum battery. Unlike the thermal states, the structural instability of passive states assures
the existence of a natural number n, for which n + 1 copies of the state can charge a quantum
battery while n copies cannot. This phenomenon can be presented in an n copy resource-
theoretic approach, for which the free states are unable to charge the battery in n copies. Here
we have exhibited the single copy scenario explicitly. We also show that general ordering of
the passive states on the basis of their charging capabilities is not possible and even the
macroscopic entities (viz. energy and entropy) are unable to order them precisely. Interestingly,
for some of the passive states, the majorization criterion gives sufficient order to the charging
and discharging capabilities. However, the charging capacity for the set of thermal states (for
which charging is possible) is directly proportional to their temperature.

Entropy is a necessary and sufficient quantity in the asymptotic limit to characterize the order
of work content for equal energetic (EE) states, but for finite quantum systems the relation is
not so linear and requires detailed investigation. Toward this, we have considered a resource
theoretic framework taking the energy preserving operations (EPOs) as free, to compare the
amount of extractable work from two different quantum states. Under the EPO, majorization
becomes a necessary criterion for state transformation. It is also shown that for EE states, the
passive state energy becomes proportional to the ergotropy in absolute sense, and it’s
invariance under unitary action on the given state makes it an entanglement measure for the
pure bipartite states.

The connection between causally inseparable occurrence of maps and charging of quantum
batteries would be worth exploring.

Related papers :

1. Tamal Guha, Mir Alimuddin, and Preeti Parashar, Thermodynamic advancement in
the causally inseparable occurrence of thermal maps, arXiv: 2003.01464, accepted in
Physical Review A (2020).
2. Mir Alimuddin, Tamal Guha, and Preeti Parashar, Structure of passive states and its
implication in charging quantum batteries, arXiv: 2003.01470, accepted in Physical
Review E (2020).
3. Mir Alimuddin, Tamal Guha, and Preeti Parashar, Independence of work and
entropy for equal-energetic finite quantum systems: Passive-state energy as an
entanglement quantifier, Physical Review E 102, 012145 (2020)
4. Tamal Guha, Mir Alimuddin, and Preeti Parashar, No-go results in Quantum
Thermodynamics, Physical Review A 101, 012115 (2020)
5. Tamal Guha, Mir Alimuddin, and Preeti Parashar, Allowed and forbidden bipartite
correlations from thermal states, Physical Review E 100, 012147 (2019)
6. Mir Alimuddin, Tamal Guha, and Preeti Parashar, Bound on ergotropic gap for
bipartite separable states, Physical Review A 99, 052320 (2019)

(P. Parashar)

<< 12