hot-state-displacement-sensing

name	hot-state-displacement-sensing
description	Quantum-enhanced displacement sensing using hot (thermal) quantum states without mandatory ground-state cooling. Identifies parity-selection and coherence mechanisms for maintaining sensitivity with mixed states, and formulates optimization comparing cooling vs direct hot-state preparation under decoherence. (arXiv: 2606.13650)
category	quantum-metrology
metadata	{"arxiv_id":"2606.13650","authors":"Piotr T. Grochowski","submitted_date":"2026-06-11","subjects":"quant-ph"}

Context

Quantum-enhanced displacement sensing with bosonic systems traditionally assumes near-ground-state initialization before nonclassical probe preparation. This paper proves that complete cooling is NOT universally optimal — sensitive probes can be generated directly from thermal (hot) states.

Core Methodology

Two Mechanisms for Hot-State Sensitivity

1. Parity Selection: Projecting a mixed probe onto a definite parity sector removes thermal suppression of displacement quantum Fisher information (QFI), which can INCREASE with initial thermal occupation.

2. Coherent Superposition: Superpositions of opposite displacements retain sensitivity through coherence between displaced components, even when the underlying state is mixed.

Protocol Classification

Hot-state protocols are classified by their sensitivity source:

• Parity-only: sensitivity from parity selection
• Coherence-only: sensitivity from coherence between displaced components
• Hybrid: sensitivity from both mechanisms

Optimization Framework

Compare initial cooling cost vs. direct hot-state preparation under realistic decoherence:

• Model decoherence as phase damping + amplitude damping channels
• Optimize total QFI per unit time (including cooling overhead)
• Show cooling is suboptimal when: (a) decoherence rate > cooling rate, (b) target displacement amplitude exceeds thermal scale

Implementation Steps

1. Hot-State Preparation: Apply squeezing S(r), number-raising a†, or cat-state generation to thermal input ρ_th(n̄)
2. QFI Calculation: Compute displacement QFI F_Q[ρ(α)] for each protocol
3. Parity Projection: Apply parity operator Π = (-1)^n̂, compute projected QFI
4. Decoherence Modeling: Apply Lindblad master equation with γ_φ, γ rates
5. Optimization: Maximize F_Q/T_total where T_total = T_cool + T_prep + T_sense

Pitfalls

• Thermal QFI suppression: Without parity projection or coherence, displacement QFI scales as 1/(2n̄+1) — vanishes for hot states
• Decoherence dominance: Hot states are MORE susceptible to phase damping; coherence-based protocols fail when γ_φ T >> 1
• Not universally better: Cooling remains optimal when (a) target precision requires ground-state fidelity, (b) decoherence times are long relative to cooling time
• Cat-state fragility: Schrödinger cat states from thermal inputs require exponentially large squeezing for large n̄

Verification

1. Verify parity-projected QFI increases with n̄ for squeezed thermal states
2. Verify cat-state coherence scales as exp(-2|α|²(2n̄+1))
3. Confirm optimization shows cooling suboptimal when γ/κ > threshold
4. Cross-check with experimental parameters from circuit QED systems

Activation

quantum metrology, displacement sensing, hot quantum states, thermal states, quantum Fisher information, parity projection, bosonic sensing, quantum sensing without cooling, coherence-based sensing