Qingtian Miao at Texas A&M University reports that extracting information from a quantum record created without entanglement demands measurements using entanglement. The work demonstrates a strict separation in how information is read based on the overlap parameter ‘p’ within the record; for 0 < p ≤ 1-1/√(2), the best separable readout approaches a success probability of 1/2 as the distance between spins grows.

This means standard measurement techniques fundamentally fail to extract long-range information beyond chance levels under these conditions, while for 0.29181 ≤ p ≤ 1, entangled measurements are required to maintain a success probability above 1/2 independent of distance.

Ising Spin Records via Local Probe Couplings

The ability to discern the relative orientation of distant spins hinges on the strength of the initial recording, with the overlap parameter ‘p’ defining a critical threshold for successful readout. Probes encode one bond label in two states, and the fidelity of this encoding, governed by the 1-p overlap, directly impacts the potential for extracting long-range information from the resulting record. A lower value of ‘p’ introduces more error during the initial recording, necessitating more sophisticated measurement techniques to overcome inherent noise. Measurements using standard, separable effects are limited to a success probability of 1/2 when ‘p’ is less than or equal to 1-1/√(2), approximately 0.293, even with classical communication and adaptive strategies.

The work establishes a clear boundary between how information is stored and how it is accessed, revealing a surprising disconnect between local creation and potentially non-local readout. However, a joint readout of the same record can maintain a success probability exceeding 1/2 by a positive amount, independent of distance, when the overlap parameter falls between 0.29181 and 1. This range, defined by the values 0.29181 and 1-1/√(2), defines a strict separation in readout capabilities.

The researchers demonstrate that a record created locally and without entanglement can, in fact, hold long-range information, but only if measurements employ entangled effects to reliably read it. The paper notes that “loops are needed for the separation between readouts, rather than for path information itself,” highlighting the necessity of entanglement for accessing information stored in this manner. The study maps the prediction advantage of this joint readout to a classical inference problem, providing a lower bound where the advantage vanishes, further solidifying the distinction between separable and entangled measurement strategies.

Probe Qubit Encoding of Bond Labels with Overlap 1-p

The overlap [p_*,p_0] gives a strict separation between the readouts. Each physical bond of an uncorrelated Ising system leaves a record in one probe qubit with two possible pure states. Their overlap is 1-p, so p controls how clearly the probe records its bond label. On the square lattice, the researchers prove a strict long-range separation. This includes every LOCC protocol, however adaptive.

Separable Records and the Task of Distinguishing Spin Directions

The best separable measurements on a square lattice approach only a 50% success rate when determining the relative direction of distant spins, as spin separation increases and for overlap parameters less than or equal to 1-1/√(2). This limit applies even when employing all local operations alongside classical communication strategies, demonstrating a fundamental constraint on extracting long-range information from these records. The work extends existing information-percolation bounds, originally developed for classical observations, to the realm of quantum probe records, providing a rigorous mathematical framework for understanding these limitations. The study defines a specific range, from 0.29181 to 1-1/√(2), where a surprising disconnect emerges between information storage and retrieval, suggesting that while the information is encoded in a separable manner, accessing it necessitates quantum correlations.

The researchers bound the squared prediction advantage of these measurements by a random connection probability on the lattice, offering a way to quantify the difficulty of discerning spin directions. The conditional records, representing the probabilities of spins pointing in the same or opposite directions, are normalized mixtures of product states, confirming their fully separable nature. The team calculated the advantage of a measurement within a defined box, then took the limit as the box size increased, ultimately revealing the system-size limit at each fixed spin separation. They clarify that “edges are independently retained, and the connection event is a path joining i and j,” explaining how the system’s connectivity impacts the ability to predict spin alignment, focusing on predicting T = $z_{i} z_{j}$ , where T equals +1 if the spins align and -1 if they oppose, each outcome being equally likely.

Success Probability Threshold for Separable Readouts: p_0 = 1-1/√(2)

The work establishes that any adaptive measurement strategy constrained to separable effects will ultimately perform no better than random guessing under these conditions. A distinct boundary emerges between 0. However, this information remains inaccessible through separable measurements. The analysis focuses on predicting the relative orientation of distant spins, where a positive prediction indicates alignment and a negative prediction indicates opposition. Within the separation window, the best separable and local operations with classical communication (LOCC) readouts approach a success probability of 1/2, effectively rendering the system unreadable by conventional means. The paper notes, “In the separation window, a receiver restricted to separable effects loses the ability to predict whether distant spins are aligned,” emphasizing the necessity of entanglement for successful readout. Local interactions, the researchers demonstrate, can create a fully separable record that inherently requires entangled measurement effects to reveal its long-range information.

Joint Measurement Advantage for p_* ≤ p ≤ 1

The work establishes that even adaptive measurement protocols constrained to local operations with classical communication (LOCC) cannot overcome this limit when ‘p’ is sufficiently low. The advantage gained from joint measurements stems from the ability to detect subtle correlations that are lost when using only separable effects. The researchers proved that any measurement family exhibiting this advantage must necessarily include entangled effects at larger distances, with at least one effect exhibiting a negative partial transpose across a cut of the probes. This finding highlights a fundamental disconnect between how information is encoded in the record, locally and separably, and how it must be accessed to achieve reliable long-range prediction. The advantage persists at every finite distance, though it does diminish as the path between spins lengthens.

Physically, the loss of advantage with lower ‘p’ values correlates to the rarity of discernible paths between distant spins. When ‘p’ equals 1, each bond label is perfectly readable, and the connection argument, that a path between spins carries information about their relative orientation, remains valid.

Positive Partial Transposition (PPT) Measurement Restriction

Measurements retaining positivity under partial transposition (PPT) face a definitive limit when discerning distant spin states, according to new work on quantum records. The research extends established information-percolation bounds to quantum probe records, demonstrating that the ability to predict spin alignment diminishes as the distance between spins increases for lower ‘p’ values. Analysis focused on square lattices using free-boundary boxes, with only bonds fully contained within the box considered in calculations. This rigorous approach establishes a clear boundary between separable and entangled measurement strategies.

Mapping Joint Readout Advantage to Classical Inference

This mapping allows researchers to determine when the benefit of a joint measurement, examining multiple probes simultaneously, vanishes, effectively setting a limit on how much information can be extracted from a quantum record. A protocol using a single round of classical communication can achieve the optimal performance for the restricted readout, mirroring the advantage gained from loops in the quantum system. Analysis of the square lattice revealed that the vertices reachable from the origin along revealed edges define a cluster, providing a means to determine when the restricted advantage is lost. This connection between graph theory and quantum information retrieval highlights the importance of network topology in information processing. This approach effectively certifies an advantage in the quantum measurement by hiding information in the auxiliary classical problem.

Probe Record Formulation: Initial States and Conditional Records

This parameter controls how clearly the probe records its bond label. The resulting record is fully separable, meaning it contains no entanglement, yet can encode information about distant spins. A receiver attempting to predict the alignment of two distant spins, i and j, faces a critical threshold. This outcome arises from the conditional records being normalized mixtures of product states, fully separable and therefore constrained in the information they can reveal. The analysis reveals a distinct boundary defined by the overlap range of [0.29181, 1-1/√(2)]. This work demonstrates that while a record can be created locally, accessing its full informational content requires measurement techniques that transcend classical limitations.

👉 More information
🗞 Reading long-range information from a separable quantum record requires entangled measurements
✍️ Qingtian Miao (Department of Physics and Astronomy, Texas A&M University, Texas, USA)
🧠 ArXiv: https://arxiv.org/abs/2611.14295v1

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