Quasiprobability Distribution for Heat Fluctuations in the Quantum Regime

Abstract

The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system. Here, we overcome this difficulty and derive the heat-exchange-fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution. Its negativities, being associated with proofs of contextuality, are proxies of nonclassicality. We discuss the thermodynamic interpretation of negative probabilities and provide heat-flow inequalities that can only be violated in their presence. Remarkably, testing these fully quantum inequalities, at an arbitrary dimension, is no more difficult than testing traditional fluctuation theorems. We test these results on data collected in a recent experiment studying the heat transfer between two qubits and give examples for the capability of witnessing negative probabilities at higher dimensions.

Minimizing Backaction through Entangled Measurements

“…That is, there is no QBA when the state is, in a sense, classical, and the joint probability is p cl ij = Tr(ρP i P j ) ≥ 0, where P i and P j are the eigenprojectors of A and A H , respectively (A = i a i P i , A H = i a i P i ). This statistics coincides with that of the measure-evolve-measure protocol, widely used and discussed in quantum transport [19,36,54,55] and thermodynamics [18,[55][56][57][58].…”

“…quantum non-demolition) measurements [1][2][3][4][5][6][7][8][9][10][11][12][13]. Besides its fundamental interest, QBA also has important consequences for the definition of heat and work fluctuations in quantum thermodynamics [14][15][16][17][18] and quantum transport [19].…”

Quantum Work Statistics with Initial Coherence

“…This fundamental bottleneck has led to efforts aimed at formulating coherence-preserving protocols for the quantification of the statistics of energy fluctuations resulting from a quantum process [ 21 , 22 , 23 , 24 ]. A particularly tantalising one entails the use of quasi-probability functions to account for such statistics [ 21 , 25 , 26 , 27 ].…”

“…Negative values of the statistics inferred following the ensuing protocol witness strong non-classicality of the overall process followed by the system [ 23 ], which are completely removed from the picture provided by TPM. In such a context, it is crucial to pinpoint the role that the quantum coherences either present in the initial state of the system or created throughout its dynamics have in the setting up of the MH phenomenology.…”

“…Several strategies beyond the TPM scheme have been pointed out in this line [ 5 , 6 , 7 , 21 , 22 , 23 , 24 , 32 ]. Here, we will consider the MH scheme for measuring work, which replaces the first projective measurement of the TPM scheme with a weak measurement [ 23 ], and thus allows for initial coherence to survive along the protocol. For an initial state , the values of work are now distributed according to where is the MH quasiprobability distribution, which can take negative values in the range when the state that we consider deviates from equilibrium [ 21 ], and goes back to the distribution associated with a TPM approach for initial equilibrium states.…”