Memory--Transport Competition in Physical Two-Bath Quantum Reset Dynamics

The gist: A seemingly natural protocol which exactly replaces the bath occupations while preserving arbitrary system–bath coherences need not correspond to a physical fermionic state, and this study constructs a two-reservoir protocol with independent, number-conserving thermal attenuators for which complete positivity and fermionic admissibility hold by construction

Memory–Transport Competition

The paper investigates the competition between coherence preservation and environmental renewal in quantum memory and transport dynamics. It shows that the coherence control is not an independent hard-reset knob, as physical attenuation necessarily modifies bath populations as well as cross correlations The model provides a microscopic, fermion-admissible benchmark for the interplay of reservoir coherence, particle transport, and energetic exchange.

Model and Implementation

The study employs a microscopic two-bath refresh operation within the quadratic SPDM framework. Key aspects of the model include:

**)&Hˆ = Xαβ a†αMαβaˆβ, M = M† (1) The number-conserving fermionic Hamiltonian is defined. 2) For a single system level 0⟩ coupled to NL and NR bath modes, M = (ω0 gL gR g†L ML 0 g†R 0 MR), Ma = diag(ωak), (2) The bath energies ωak and couplings gak are allowed to be arbitrary at this stage. 3) Defining the annihilation column a = (ˆa0, aˆL1,..., aˆRNR) T, the exact Heisenberg equation reads i∂taˆ = Maˆ, so a(t) = e−iMtaˆ(0). 4) The SPDM is Cαβ = ⟨a†β aα⟩. Its fermionic admissibility criterion is 0 ≤ C ≤ I; for quadratic numberconserving dynamics its exact unitary update is C−n = UC+n U†, U = e−iM τ (3). 5) Let tn = nτ. We write C+n = C(t + n) for the state immediately after the nth refresh and C−n = C(t − n+1) for the state immediately before the next refresh; hence one cycle is first the exact unitary update C−n = UC+n U† and then the ancilla contact C+n+1 = R(C−n) (3). 6) Each two-mode transformation is an orthogonal rotation in one-particle mode space, and is therefore induced by a number-conserving unitary on the two-mode Fock space. 7) The exact post-refresh covariance is C+n+1 = KC−n K + D (7). 8) The attenuation parameter necessarily changes both coherence retention and the refresh strength 1 − η2a: these are linked controls, not independently selectable thermodynamic interventions. 9) At ηa = 0 the incoming fresh ancilla replaces every bath eigenmode on side a, while the pre-contact bath mode exits through the outgoing ancilla port. 10) Intermediate values both damp existing crosscorrelations and partially restore occupations. 11) Full bath replacement is recovered at ηa = 0, but then that side’s system–bath coherence must also vanish. 12) The construction is side-local (left and right bath operations are independent), but it is not automatically implementable by contact with just the endpoint site of a spatially local chain. 13) The parameter extremes have different microscopic meanings. 14) At ηa = 1 no bath mode on that side is renewed or attenuated. 15) Full bath replacement is recovered at ηa = 0, but then that side’s system–bath coherence must also vanish. 16) Unlike a hard replacement with retained cross correlations, Eq. (7) has an explicit quantum-channel realization. 17) The attenuation matrix obeys∥K∥ ≤ 1 and U is unitary. 18) In finite dimension the condition r(A) < 1 is equivalent to the absence of an eigenvector of U that lies entirely in the undamped subspace H1 = ker(I−K2). 19) We give the necessity and sufficiency proof in Appendix A. 20) The exact terminal-blockade theorem applies to this number-conserving refresh operation, valid at arbitrary τ and finite bath size wherever a stationary state exists. 21) The exact microscopic identity makes ∆Na proportional to the refresh probability 1 − η2a but leaves its prefactor state-dependent. 22) The signed energy delivered to the fresh ancillas, whose mode energies match those of the reservoir modes, is Qa = Tr[Ma(C−aa,fp − Caa,fp)], JE = QL + QR τ (20). 23) The incoming and outgoing ancillas are mode matched. 24) These are exactly Eqs. (27) and (28), including the contribution from intra-cycle transitions at ηa = 0. 25) Bath–bath off-diagonal covariances first affect the displayed mode-resolved diagonal transfers beyond the order kept here for fixed ηa < 1. 26) The coherence maximum occurs on the displayed ηR = 0.995 boundary. 27) The window-constrained value Cmem = 0.03523 is therefore not the maximum over the full physical retention range. 28) The peak drifts toward full retention as bath size grows. 29) These numerical operating-point separation survives each reoptimization, but the smaller-size energy optimum is less stable. 30) The coherence maximum occurs on the displayed ηR = 0.995 boundary. 31) The peak along the fixed-ηL cut is located near 0.99687, 0.99839, 0.99877, 0.99896, with coherence 0.03478, 0.04450, 0.42524 at N = 14 (35). 32) These are numerically optimized one-dimensional cut maxima, not rigorous global extrema. 33) The coherence maximum occurs on the displayed ηR = 0.995 boundary. 34) The memory optimum within the specified scan region occurs at its upper ηR = 0.995 boundary. 35) The coherence maximum occurs on the displayed ηR = 0.995 boundary. 36) The coherence has a narrow maximum within 0.97 ≤ ηR ≤ 1 that shifts toward full retention as Na increases. 37) This maximum lies outside the range ηR ≤ 0.995 used for the operating landscape in Fig. 1. 38) The affine equations are algebraically well defined, and some solutions satisfy the covariance bounds<ref:2610.

1. This AI system can optimize quantum memory operations by identifying operating points that maximize retained one-body coherence, particle throughput, and signed energy transfer simultaneously within a two-bath refresh protocol. This allows for the design of memory protocols that balance these competing objectives according to the microscopic, fermion-admissible operation.

2. The AI can predict the exact stationary through-current under specific reservoir conditions by using the exact terminal-blockade lemma, which states that the net stationary through-current must vanish if either reservoir is entirely unrefreshed. This enables the design of quantum devices with guaranteed particle blockade at high retention boundaries.

3. The system can determine the physical limits on quantum memory resources by calculating the exact memory–occupation bound, which shows that retaining coherence is necessarily limited by the occupation and Pauli exclusion, independently of reservoir spectra, reset parameters, or cycle duration. This prevents over-optimizing coherence at the expense of particle throughput.

4. The AI can assess whether a proposed algebraic hard-block prescription is physically implementable by checking both Schur-complement inequalities (37) and (38), which are the necessary and sufficient physicality conditions for fermionic covariance matrices to be allowed. This ensures that theoretical models do not propose non-physical states.

5. The system can provide a microscopic accounting of thermodynamic work by calculating the signed net work, P Wsw = Delta Eint,refresh, which is the full retained plus ancilla energy change, distinguishing it from simple heat flow magnitudes for resource-constrained optimization.

Coherence preservation and environmental renewal offer competing ways of controlling quantum memory and transport. We show that a seemingly natural protocol which exactly replaces the bath occupations while preserving arbitrary system--bath coherences need not correspond to a physical fermionic state. We instead construct a two-reservoir protocol with independent, number-conserving thermal attenuators, for which complete positivity and fermionic admissibility hold by construction. Physical attenuation necessarily modifies bath populations as well as cross correlations; the coherence control is not an independent hard-reset knob. Quadratic dynamics reduces the stroboscopic problem to an exact matrix fixed-point equation without a weak-coupling or Markov approximation. Analytically, coherence retention enhances the leading short-cycle transfer rate, including the complete-erasure limit; no general endpoint-vanishing theorem exists. An exact stationary continuity theorem forces the through-current to vanish whenever either reservoir is left entirely unrefreshed, although no analogous theorem suppresses it at complete erasure. For biased structured reservoirs, exact finite-chain calculations display distinct coherence-, current-, and signed energy-transfer operating points; a resolved high-retention boundary layer exposes strong finite-size sensitivity of the coherence peak. The model provides a microscopic, fermion-admissible benchmark for the interplay of reservoir coherence, particle transport, and energetic exchange.